Before you start telling me that guide is wrong, please do check if you have mods installed. Several of them make the 1st choice the correct answer in all riddles.
Created this section because I saw several people having problems with that.
Examples of mods that do that:
https://gtm.steamproxy.vip/sharedfiles/filedetails/?id=3041058449
https://gtm.steamproxy.vip/sharedfiles/filedetails/?id=3090736625

Sorted in alphabetical order, number corresponds to the line you need to choose.

A sudden move - 3 (Fit)
Arrow through the heart - 2 (Must)
Beyond the blue mountain - 4 (Out)
Brothers and sisters - 1 (Catch)
Collusion between the top and the bottom - 2 (Card)
Extra generous - 3 (Return)
Hand without an inch of iron - 1 (Control)
January 7th - 2 (Fat)
Lost it's heart - 1 (Total)
One big two small - 4 (Nai)
Out of place - 3 (Stand)
The emperor's new clothes - 4 (Attack)
The sun rises in the east - 1 (Nine)
Thousands of words - 2 (Enough)
Wave Goodbye - 4 (Army)

Couplet matching with him gives you wisdom, exp, sect contribution and a bit of favor with him.

A boat full of moonlight sails away, - 1
A body turns into a thousand miles, - 2
A flute, a sword, a lifetime's intention, - 2
A fragrance fills Chang'an, - 3
A hall full of flowers drunk three thousand guests, - 1
A meteor white jade inserted in the waist - 1
Climb high and look far into the world, - 2
Dance with the lotus sword, - 3
Drinking horse across the autumn water, - 3
Free and easy in the world for ten autumns, - 1
Heaven and earth, wind and dust, a three-foot sword, - 1
Heaven creates me, I must have my use, - 4
Honorable death intimate - 2
Jinghua makes friends with all the talents - 3
Laugh and go out, - 2
Life is full of joy, must be enjoyed, - 2 (maybe 4, I'll check later)
Peach and plum spring wind a cup of wine - 2
Peach blossom seeks the sword guest, - 3
Press the sword to clear the eight poles, - 4
The roc rises with the wind in a day, - 1
The small boat is gone from here, - 3
The whale has not swallowed the sea, - 3
The world is like a tide, people like water, - 2
The world's wind and clouds come out of my generation - 2
Travel a thousand miles with a sword - 2
Who knows the hardship of the border, - 4
Why not carry the Wu hook, - 1
Will be on the top of the mountain, - 3
Yellow sand battles wear golden armor, - 2
Young people take risks as if they were flat ground, - 2

Periodically challengers will loaf at the entrance of the sect, it can be either 2 dudes looking for a fight or 3 scholars with a couplet matching challenge.

A big belly can tolerate things that the world cannot tolerate - 4
As the heavens add to the years, people add to their lives. - not 4
Because of the lotus, we get the lotus root. - 3
Blue Mountain is fortunate to bury loyal bones. - 3
Cordyceps sinensis has nine layers of skin - 4
Green and red everywhere, swallows and orioles everywhere. - 4
No tin in Wuxi, no tin in Wuxi Mountain. - 2
One sheep leads two lambs - 4
The New Year brings extra celebrations. - 4
The bright moon in the sky illuminates the three thousand realms. - 1 or 4 people are drunk in the spring breeze on the twelfth floor (gotta actually read the answers)
The chrysanthemum in golden autumn defies frost. - 2
The door faces a thousand bamboo. - 2
The green water has no worries, but the wind wrinkles its face - 1
The jade swallow welcomes spring, and spring always comes. - 4
The landscape of thousands of miles is like a brocade. - 2
The lights of thousands of households are as bright as the autumn moon - 2
The moon under the water is the moon in the sky - 3
The silkworm is the insect of the world. - 3
The sky is a chessboard and the stars are the pieces, the sun and the moon compete for light. - 2
The spring lanterns of thousands of households celebrate the Lantern Festival - 4
The thatched cottage leaves a legacy for future generations. - 4
The tower lights up, layer upon later of Kongming - 1
Thinking of getting old before getting old. - 1
This wood is firewood from the mountains - 3
Two, three, four, five. - 3
Who was it that crawled through the dog hole to steal peaches yesterday? - 3

So. There's kind of an alternative method of joining (or at least being granted access if you don't have enough fame) Confucian sect, and that is becoming a certified scholar. There's also an achievement tied to the exams. First of all you need (maybe not necessary?) to go Confucian sect, talk with the old man outside the gates, try to walk in, get denied (unless you have high fame), talk to old man again. He'll tell you how to become a scholar:

1) Pass the exam at Dragon Library in Chuxiang City. To do that, first you need to impress the dean by coming to him for like 5-6 days (didn't count) and do the usual couplet matching. After that he'll confess that he misjudged you and offer you to try the exam. Go into Government office where you'll be examined, do note that it will take 1 day. Result of the exam will be out in 3 days and it will be sent to you by a pigeon.

2) Pass the exam at Imperial School in Daling City. Same thing, different city. The result is going to be posted on the mission board.

3) And finally, it's time for the final exam at Confucius temple. Gatekeepers will ask you for some couplets before granting access. Enter through the gate, note the statue that will give your entire team +50 Intelligence EXP, which will allow you to raise everyone to 10 INT if so desired, enter temple, speak with sect master, get ready for exam.

If you want to get the achievement and traits, you need to explicitly get Top Exam Result for second and third stages of certification. After becoming a certified scholar you'll be able to teach children at Confucius temple.

What's peculiar about exams is that on the final question there's no indication of it being wrong or right. You'll know only after you get exam results, with it saying "you passed" if you got the wrong answer on the last question or "you're the top examiner" if you got it right. Those final questions are set in stone and there's like 2-3 of them in each exam. It's a bit hard to verify answers, but I'll update those later.

A journey of a thousand miles begins with a single step - 3
A long journey tests a horse strength - 4
A tree as big as a men’s embrace - 3
At four years old he could yield pears - 3
At the beginning human nature is good - 1
Confucianists confuse the law with their writhing - 2
Cruel world, treating all things as straw dogs - 4
Honourable and magnanimous - 2
Honorable yet different - 3
If a father does not teach a son he is to blame - 1
In poverty, one focuses on self improvement - 3
It’s easy to paint the skin of a tiger, but not its bones - 2
Jade if not polished, does not become a tool - 2
Learning without thought is labour lost - 1
Man follows the earth, the earth follows the heaven - 4
Not teaching - not 2
Planning behind the curtain - 1
Poor self-improvement - 3
Respect the old and extend it to others - 2
The highest good is like water, water is good at - 1
The mountain does not tire of height, the ocean does not tire of depth - 3
The movement of the sun and the moon as if it were among them - 2
The ospreys cry - 3
The three powers are heaven earth and man - 1
The waves behind drive on those before - 3
The way of teaching, value is focus - 4
The wise man is as good as water, great ocean manual - 3

A gentle men dies for his intimate - 2
A good farmer does not stop ploughing because of drought or flood - 3
A thousand cups are too few when you meet your intimate - 4
Drain the pond to fish, won’t you catch them? But next year there will be no fish - 3
Having ten horses is not as good as having one bole - 3
He who knows others is wise, he who knows himself is enlightened - 1
If the year is not cold, you won't know the strength of the pine and cypress - 4
If you don’t climb high mountains, you won’t know how high the sky is - 1
Not seeing oneself therefore Enlightened - 4
Persist and give up, rotten wood will not break - 2
Piling up soil to form a mountain, wind and rain will rise - 4
The frog in the well cannot speak of the sea, because it is confined to the void - 3
Three years of good deeds, known by few - 1??? (final question)
Under the fragrant bait, there must be a hanging fish - 2 (final question)
Without indifference, there is no way to clarify ambition - not 4 (final question)

A big belly can tolerate things that the world cannot tolerate - 2
A thousand cups of fine wine become self-knowledge - 2
A tiger drink a cup and gets drunk in the mountain - 2
Actions without shame under heaven and earth - 2
All mountain bow down to it - 3
All mountains are paintings - 2
Among men, a fine horse gallops a thousand miles - 2
Ancient and modern wonders belong to the rocky gorges - 2
Ask the green ox who rode away - 2
Blue mountain does not ink a thousand autumn painting - 3
Clouds mindlessly emerge from the mountains - 4
Destined to meet from a thousand miles away - 1
Don’t talk about worldly affairs facing Blue Mountain - 3
Draw a sword to cut water, water flows more - 2
East, south, west, north - 2
Favourable wind and rain - 2
Fortune comes twice, today it comes - 2
Good bird choose trees to nest - 3
Good books are not tired of reading and re-reading - 1
Great ocean Manual, tolerance is greatness - 1
Heard that the mountain stones have no false colours - 1
Holding a three foot longquan sword - 1
Horse neighs when it meets a good master - 1
How can a sparrow know the ambitions of a swan - 4
How can life always go as one wishes - 4
Hungry chickens fight for beans - 3
Ideal not to enjoy sweet wine - 1
Jade can be shattered but its whiteness cannot be changed - 2
Less water reveals the sand - 1
Moon under the water - 1
Nurturing the righteous qi of heaven and earth - 3
One flower, one Buddha, one world - 2
Peace is originally set by the general - 2
Proud soldiers often lead to defeat since ancient times - 2
Righteous often slaughter the god breed - 3
Small temple without monks, wind sweeps the ground - 4
Since ancient times, arrogance has often lead to defeat - 2
Teach your children and grandchildren to first teach yourself - 3
Ten thousand mountains to worship - not 1
The body is a buddha tree - 2
The clear wind intends to keep me from staying - 1
The moon under the water is like the moon in the sky - 4 The person in the eye is the person in front
The sea is tolerant of all rivers - not 3
The sea is wide enough for fish to leap - 1
The sharpness of a treasure sword comes from grinding - 3
The sound of wind, rain and reading enters the ears - 3
The tomb door is locked by misty clouds - 1
The wind sweeps the ground when the temple is small and there are no monks - 4
There are no mountain and rivers in the sky - not 2
There are no mountains and rivers in the sky - 4
Thousand autumns of ink and brush amaze the world - 3
Three generations of a family buried in the same soil - 3
Three religions and nine school of thought all return to the great path - 1
Water flows from the jade ring - 1

A horsemen in the red dust makes the princess laugh - 1
A moment of spring night is worth a thousand gold - 2
After the rain in the empty mountain - 4
Clouds think of clothes, flower think of faces - 3
Died before the battle was won - 3
Having done the deed, I leave without a trace - 3
I urge you not to cherish your golden robe - 2 (final question)
I urge you to drink another cup of wine - 3
I was born with talent it must be useful - 3
In the dead of night, I listen to the wind and rain - 3
Kill a man every ten steps - 2
Laughing to the sky, I walk out the door - 4
One must enjoy life when successfull - 3
Once having seen the vast ocean, one can't be content with a pond - 2
Old friends bid farewell to the yellow crane tower - 2
Rain pours down during the Qingming Festival - 1
Raise a cup to invite the bright moon - 4
Red beans grow in the south - 1 (final question)
Shoot the man before shooting the horse - 1
Spring wind blows for ten miles in Yangzhou road - 3 (final question)
Startled awake from a dying illness - 3
Taking a leasurly look at the flowers, I don't look back - 2
The broken spear sinks into the sand, the iron is not yet destroyed - 2
The lonely smoke in the vast desert goes straight - 1
The window contains the thousand autumns of the west ridge - 3
Today's people don't see the moon of ancient times - 1
Twenty-four bridges on a bright moonlit night - 2
Two orioles sing in the green willow - 2
Where is the tavern, I ask - 1
White hair mourns the bright mirror - 4

A bird about to die, its song is sad - 3
A man must degrade himself before others will degrade him - 2
A room doesn’t need to be elegant - 4
Calligraphy painting, chess, and music shine through the ages - 3
Do not worry about scarcity, but about inequality - 1
Five flower horse, thousand-gold fur - 4
Four hundred and eighty temples of the southern dynasty - 3
Having seen through human nature, the autumn clouds are thick - 3
Heavens timing is not as good as the geographical advantage - 1
Honourable cherish virtue, while villains cherish wealth - 2
Honourable is open and upright, while the villain is always in a hurry - 1
If one’s body is upright, one will act without being ordered - 2
If the name is not correct, then the words will not be smooth - 4
In a low position, I dare not forget to worry about the country - 3
It's hard to win when you meet a good opponent in chess - 2
Learn widely, ask carefully - 3
Learning without thinking causes confusion - 1
Left to lead yellow, right to hold blue - 2
Life between heaven and earth, like a white horse passing a gap - 2
Poetry and books are not medicine, but they can cure vulgarity - 2
Scooping up the moon in the water - 3
Since ancient times talented people have faced many hardships - 3
The art should begin with diligent learning - 3
The clear wind and bright moon are priceless - 2
The highest good is like water - 2
The limit of a strong crossbow - 2
The mountain has wood, the wood has branches - 2
The roc flies with the wind in one day - 1
The tree that can be embraced grows from a tiny sprout - 2
The wise men worries a thousand times, there must be a mistake - 3
The world is bustling, all for profit - 1
There is an ancient pine at the door, and nom messy stones in the courtyard - 1
When Three people walk together, there must be a teacher among them - 1
When poor, one should improve himself - 3

P.S. My notes got scrambled, so both the entrance test and exam are in the same section. Just Ctrl-F.

As was mentioned before, after becoming a certified scholar (and probably joining confucian sect) you can teach children (clarify doubts) in the morning/day.

What are the "three obediences" in "three obediences and four virtues"? - 2
What are the four books in "Four Books and Five Classics"? - 1
What does "coming but not going is impolite" mean? - 1
What does "cup" in "seeing a bow in a cup as a snake" mean? - 4
What does "joy" in "it's better to enjoy together than alone" mean? - 2
What does the "autumn" in "a day without seeing you feels like three autumns" mean? - 3
What does the "autumn" in "one day three autumns" mean? - 4
What does the "cave" in "without entering the tiger's den, how can one get the tiger's cub" mean? - 3
What does the "cry" in "a cry that shocks everyone" mean? - 3
What does the "drum" in "First blood" mean? - 1
What does the "eye" in "painting the dragon and dotting the eye" mean? - 4
What does the "firewood" in "sleep on brushwood and taste gall" mean? - 2
What does the "flower" in "a flower, a world" mean? - 1
What does the "gold" in "a word worth a thousand gold" mean? - 2
What does the "morning" in "the plan of a day lies in the morning" mean? - 4
What does the "peach and plum" in "peach and plum do not speak, but a path is formed beneath them" mean? - 2
What does the "pot" in "break the pots and sink the boats" mean? - 2
What does the "sea" in "all within the four seas are brothers" mean? - 2
What does the "see" in "seeing is believing" mean? - 3
What does the "shoe" in "Zheng people buy shoes" mean? - 3
What does the "silk" in "the spring silkworm may not stop until death, the silk it spits out until the end" mean? - 4
What does the "water" in "a belt of water" mean? - 2
What does the "worry" in "those who do not worry about the future must have immediate worries" mean? - 3
What is the origin of eating mooncakes during Mid-Autumn Festival? - 2
Which book does "A journey of a thousand miles begins with a single step" come from? - 2
Which dynasty did the "Spring Festival" originate from? - 4
Which three countries are in "The Romance of the Three Kingdoms"? - 1
Who is the author of "Sing loudly in the day and must be drunk"? - 3
Whose residence is the "thatched cottage" in "three visits to the thatched cottage"? - 3
Why do we eat Tangyuan during the Lantern Festival? - 1
Why do we race dragon boats during the Dragon Boat Festival? - 3
Why do we wear sachets during the Dragon Boat Festival? - 1

After getting 2 top examiner traits, you'll be able to introduce yourself as a scholar when saving the Emperor from imprisonment. After that you need to initiate fights with generals (enemies with black armor and staff), which will initiate a cutscene where MC says a poetry line. Do that 4 times (out of 6 generals), while taking care not to aggro them by fighting regular mooks it was fixed in an update, just wander around until you find 4 fights with emperor present in them. After that go towards the exit. Emperor will praise your literary abilities and you'll get the trait.

It's a seasonal achievement, so you need to set your date to June 22 on your pc, then go to tavern in Chuxiang city (not the hotel where you can sleep), talk with the owner, he'll ask you 5 questions, then after you answer them all, he'll send you to Lin'an city's pier. There you'll see an npc that will ask you to choose your fighter (I won with the top one, I think). There's time to save between fights, so abuse that. After winning 3 times, you'll get the achievement and a bit of fame.

What are the five poisons to be eliminated during the Dragon Boat Festival, including snake, scorpion, centipede and toad? - 1
What does the "kanji" in Dragon Boat Festival mean here? - 2
What flavor is the zongzi in Lin'an City? - 1
When is the Dragon Boat Festival? - 4
Which one is not another name for the DBF? - 3