Spellbook Demonslayers has a lot of stats, numbers and effects interacting. It's not always obvious which interact, which don't, and how things fit together.
So here's some things I've tested (since the prologue), read about and observed.

Disclaimer: the game gets updated a lot! It's entirely possible this guide will be outdated by the time I hit publish! (Not complaining, but please take a breath Xendra! Launch burnout is a real thing!)
Also, I could just be wrong about some parts. Let me know in the comments!

Let's start with some short, general things that aren't particularly explained but also don't need too much explanation.

Stats
Those things on the bottom of your screen, what do the less obvious ones actually mean?

• Banish lets you make one option not show up. This includes in chests, but does not include a Spell's upgraded version unless that's what you Banish (and then it won't include the basic version).
  
• Damage is straightforward; all % increases add to eachother. But "Chance to do triple damage" multiplies, just like crits (and a few other effects) do.
  
• Cast Speed determines how long it takes for a spell to fire (play the animation). Spells also have a cooldown after they're done before it can start to cast again, that mostly goes down with spell levels. Cast Speed also affects how fast damaging areas such as Burning Ground or Tail Wind lvl 4 tick their damage.
  
• Crit Chance determines the chance your numbers become yellow and be bigger. Above 100% they become orange and EVEN BIGGERER. Currently unsure what happens above 200%.
  If a projectile rolls a crit, every hit that projectile makes will be a crit. But it's rolled per projectile, not per spell.
  
• Crit Multiplier is how much bigger your yellow crits are. Orange crits double the extra damage; for example if we have 2x (or +100%) our white dmg is 100%, yellow is 200% and orange is 300%. This can still be tripled or modified in other ways as normal, and afaik everything can crit (yes explosions etc). At 5.7x multiplier your execute (from the lvl 4 upgrade) is at maximum by the way.
  
• Health is how much damage you can take before you die. Flat numbers get added first, then the result is multiplied by any percentages you have (Juggernaut gives more Health per level, or less if you have any -%). Max Health can't go below 1, even with rounding, but current Health can (you can be alive at "0").
  
• Regeneration heals you that amount every second. Every heal is actually added to this, but translated to the heal/second format even if the source doesn't show it that way.
  Note that the number next to your hp bar is how much you're actually healing, but in your stats is your actual Regeneration (which certain effects scale with, in case not all your Regen goes to your hp). It actually ticks for a fraction of this number multiple times per second.
  
• Armor is a flat damage reduction; if you would get hit for 100 damage with 10 armor you take 90 damage. This applies before any % damage bonus the attacker would have; if that previous enemy had +100% damage you would take 180. Negative armor works the same, but you take that much more damage per hit.
  This works the same on enemies, and scales over time for them.
  
• Projectiles and their stats (# of projectiles, pierce, chain, speed+range, size) get next section because there's too much to explain.

Other

• Elite enemies buff everything around them in a certain radius, the effects differ but depend on the kind of elite. Knockback resistance is common to several variants it seems. Their buffs scale with time, yours do not.
  
• The Timer goes down until you hit endless/timed. At 0, all enemies from thereon get buffs and they get them again every 13 minutes in addition to their regular scaling stats. A big one is that they get a % damage reduction. I don't think it can hit 100% (I think it keeps multiplying in on itself), but if your damage suddenly drops like a rock this is why.
  
• Stacking effects. A lot of effects are described similarly, and you can stack them: if your spell instantly kills enemies below x% hp and so do your crits AND you get a crit with that spell, you add the numbers together and execute from up to 60% hp. If an Explosion kills an enemy and enemies explode when they die, there will be another Explosion and that can keep happening. If they happen to be frozen they can Shatter at the same time too!
  
• Multiple copies of spells. You need to evolve (level to 6) the spell you want a copy of, then the base version will show up again to pick. Then the evolved version needs to get to level 10 so you can evolve your new version. Then repeat that until you're done (for the achievement you need to evolve the 4th copy too). Doesn't seem like you can copy Illegal spells.

Basically everything that does damage is a "projectile". Including explosions, shatters, burning ground, areas, shields (these are areas), you name it. Sigils and Thrones are NOT projectiles, but the damaging effects they cause ARE.
But not every projectile is affected by the projectile stats, so let's go over what the stats do and when.

Projectiles (count)
Adds that many projectiles to your spell (and adjusts the firing speed to compensate). This makes it better for spells with a low projectile count (if you normally fire 1, adding 1 is +100%. But if you fire 20, you got +5% total damage). But the lvl 4 upgrade is better if you have many (base, so starting) projectiles.
This affects basically anything that moves on it's own and the number of times a sigil will hit.
No effect on explosions, shatters, lightning procs (but works on lightning from sigils and possibly the Throne areas?) or areas (but a lot of areas are spawned by moving projectiles which ARE affected).

Pierce
Your projectiles will pierce that many more enemies IF there are enough in range to do so. This is on top of any Pierce they might already have, which for all the areas is effectively infinite.
Pierce always happens before Chain, if you have too much Pierce you might not Chain at all if there aren't enough enemies in range.
"Base Damage per Pierced enemy" applies AFTER all your pierces are done, so only on your chains.

Chain
After a projectile can't Pierce anymore, it will Chain to up to this many more enemies IF they are in range.
This can technically affect explosions and everything (their damage is affected by the "+dmg per remaining chain" lvl 4 upgrade), but since they can't move they won't ever actually Chain (if enemies could be in exactly the same spot it might work).

Proj. Speed (and Range)
All projectiles travel for a set time, so the Speed of it affects how far it goes. Only affects things that do move to begin with, so not explosions and things like that.
Affects how fast Shields rotate.

Proj. Size
Affects everything except: Tail Wind lvl 4 and Shields.
Yes you can make large explosions, burning ground. Basically go nuts.

Knockback
If it does damage it does knockback. It always knocks enemies directly away from you, even if a projectile chained back in your direction (unless Black Hole, where it's reversed).
Enemies gain more and more resistance to it depending on the clock (they also gain speed) but won't ever become completely immune.

It's not always immediately obvious how something works mechanically. You can probably figure it out between the Spell description and the previous sections, but for when you can't there's this section.

FWIW, imo this part gets a little extra spoilery. If you'd prefer to discover cool interactions and synergies on your own, skip to the next section.

Explosion, Shatter, Lightning, Slash
These are all projectiles that are spawned somewhere, through various effects, that all function the same. They are a "Projectile" that appears somewhere with infinite Piercing and 0 speed, so they hit everything in their area but can't be made to move or chain.
They essentially function the same, but some can be buffed by name. You can tell which is which from the identical shape, even if the colour is different (a green Explosion is still an Explosion).
Second Law can shut off their Piercing.
Even though they cannot chain normally, you might still see chain-explosions (and Shatters and Lightning, but not Slashes as nothing procs it on kill) but these have nothing to do with the Chain stat.

Spells
Not listing every one, since a lot work similarly you can figure them out by looking at other Spells.

• Dynamo fires two projectiles, starting right and then left. It adds extra projectiles in alternating order (first to the right, then left). Since the lightning it procs on kills is still part of the spell, that lightning can proc more lightning if it kills.
  
• Ghost Bullet will always do it's Chains, when it runs out (misses), if there's something to Chain to. It only Pierces before the first Chain.
  
• Spectre Bullet gains infinite Piercing, but is otherwise the same. Second Law works (but why would you?).
  
• Icicle first fires regular projectiles that work normally. Then a Frost Orb with infinite Piercing, if this can't Pierce through Second Law, it can Chain. Extra projectiles don't work on the Orb, but everything else does.
  
• Tome Dust fires many projectiles. If you get under -100% Projectile Speed, it inverts to shoot forwards (like Eye Popper).
  
• Armageddon Sigil designates a target to hit with several bursts of flame (not Explosion), affected by +Projectiles. The bursts are unmoving projectiles with infinite Piercing (Chain and Speed do nothing). Anything killed by the spell Explodes. Since it's still part of the spell, the Explosions set off more Explosions if they kill.
  Sometimes decides to live at the screen edge for unknown reasons, otherwise picks targets based on what touches the sigil graphic.
  
• Energy Cleave is Icicle with auto-aim, but it's Orb (Slash) doesn't move and isn't an Orb.
  
• Assault Sentinel shoots regular projectiles. The Sentinel touch-damage is only affected by Damage, Crit, Knockback and probably Cast Speed.

The Malice system, also known as Speed & Difficulty or Difficulty Settings, has a lot of nuance. So lets get into some of that.
Generally, more Malice seems intended to mean "more difficult". But that's not actually the way it always works out.

First of all, you gain more Malice buffs depending on how much you buff the enemy stats. Those are clearly positives for you. Most are straightforward, but hard to get elsewhere so they can be very valuable.
Only one actually needs an explanation, and that's Levelup Healing: if you have a bonus to this you gain that much of your max health every time you level up, applied to Regeneration, over 3 seconds (so your Regeneration will increase by 33% of that number for 3 seconds). This interacts like any Regeneration would, as does all healing.

Speed & Difficulty
These are the Difficulty Settings that... might make things more difficult.
Let's start with... not actually one of those!

• Player & Enemy Speed, the slider on the Choose a Stage screen, amplifies both your and enemies' speed an equal amount. It's symmetrical! ...except you're incentivised to stay in certain areas while your enemies are not.
  This just makes the game harder, and you don't even get buffs for increasing it.

Now for the actual settings:

• Spawn Speed makes new enemies appear faster; if it would normally add 1 enemy every 1 second, this can make it 1 enemy every 0.5 seconds. More enemies, but that also means more exp for you and tighter groups for your area damage.
  Only harder if you don't have that area damage, otherwise it may even be easier.
  
• Enemy Speed makes enemies move faster. This makes it harder for you to dodge, but also gets them to your Spells (and so hopefully their death) faster.
  Only makes things harder once they get faster than you and/or you can't kill them fast enough.
  
• Enemy Damage increases how hard they hit, but after your armor takes effect. This also means negative armor values affect you more.
  Only harder if you get hit in the first place, otherwise it doesn't matter and is some free Malice.
  
• Knockback Resist means enemies don't get knocked back as far as they would be.
  Only harder if you had to rely on Knockback to survive, but that is the most common way to play I've seen even if you don't realise you're doing it. This may help you if you pick up Black Hole though.
  
• Health means enemies take more damage to kill.
  Almost always harder since you just need to do more damage. Though a few things scale off Enemy Health, so things like Shatters will just do more damage.
  
• Invincibility Penetration turns your invincibilty to mere damage reduction instead. This also affects the Second Chance upgrade (which makes you invincible and sets your hp to 1 if you would have died) meaning you immediately die on the next hit (but without it you would have died already).
  Only harder if you even get hit, unless you're playing a tank build that wants to get hit to deal damage. That one actually likes this!
  
• Empowered Elites means their buffs do more, including to enemies around them.
  If this makes things harder depends on the type of Elite and how well you can deal with that particular type, but since you'll probably see every type this is almost universally bad for you.
  
• Clock Speed makes the clock move faster. This means anything determined by it happens more quickly, but not everything is affected by it. Enemy movement, spawn speed and amount stay normal, but stronger enemies appear sooner and enemy stats scale up quicker. Elites and Smuggler Shrines appear sooner, and you'll get to timed/endless mode faster.
  Always makes things harder: your stats are unaffected and you have less time to level up.
  
• Enemy Amount is the opposite side of Spawn Speed, and everything said there applies here. If it would normally add 1 enemy per second, now it adds 2 per second.
  Note that combining this with Spawn Speed can more than quadruple the amount of enemies.
  Exactly as much difficulty increase as Spawn Speed, which again might be a negative number depending on your build and playstyle.
  
• Shrine Kill Requirement means you need that many more kills to activate all Shrines.
  Technically always harder, but how much harder it is depends heavily on your other settings (much easier to get double the kills when there's quadruple the enemies!).

The great thing about this difficulty system is that it allows you to tailor your experience to what you want.
As I've highlighted above, certain settings may actually be making the game easier on you. And if you really know what you're doing, and have a build planned, you could run something like 50 Malice without actually setting yourself back. Conversely, the hardest version of the game is probably around 30-40 malice for most people, but you'd have have to find the modifiers that affect your playstyle the most.

Anything that didn't fit in the other sections.

• Slows are all multiplicative, you can not make enemies stop moving.
  
• Some Illegal upgrades can't stack with themselves, only the ones that give you + or - some stat. Stat conversion upgrades also don't stack (ie: 2x Second Law won't add your speed to your knockback twice).
  
• Smuggler's Shrines don't shrink or go away, complete them whenever you want. The same is true for the first shrine of the game, you could save it for later.
  
• Rerolls are weighted towards things you didn't pick yet (at this levelup) if available. Last I checked it's possible to reroll everything away and not get anything for your level.
  
• Elites are Frozen for a much shorter time, you also can't re-proc Freeze on something that's already Frozen. While an enemy is Frozen, it also won't damage you.
  
• Many spells have upgrades that buff ALL similar effects (such as Indra's Sigil buffing all other Lightning Bolts, like from Dynamo for example).
  
• As I touched on earlier, there's Cast Speed and Cooldown reduction. They both basically do the same (spell go vroom), but if you somehow ended up with a lot of one and not the other you may have less vroom than you'd expect. Since Reverberation gives both stats and most spells get cooldown reduction when leveled up, it's unlikely to come up unless you're looking for it.
  
• Many numbers are tracked properly but rounded for display; you might be alive at 0 hp because you're actually at 0.1, or the "triple damage" number might be not exactly 3x the normal number because you actually do 20.5 rounding to 21 (so the 3x displays as 62 but does 61.5).
  
• Some numbers can go into the negatives, and mostly(?) work as you'd expect they should: -100% damage would mean you do no damage, -100% projectile speed means it doesn't move. But below -100% speed can actually invert the way (some, mostly aimed) projectiles shoot. At exactly -200% shields won't rotate, and below that they'll spin the opposite way.

And that's about it. Please let me know in the comments if I'm wrong about anything, or if you have questions I didn't answer.