Answers:
1) The medals are an indication of how many rounds that player has not lost. Medals can only be gained by winnning a round. If you lose a round you lose any medals you picked up. Not winning and not losing does not change your medal count. There is a maximum of 3 medals next to your character.

2) They are not all the same. However since B.U.T.T.O.N. was created for a one button competiton all of the final conditions are some kind of variation of win/lose press or hold the button. As you may have noticed the conditions in the middle vary. Some are Frequent and some are extermly rare. It's kind of hard to put a number on exactly how many there are since some conditions are procedurally generated.

3) All 18 should show up. Only 5 have are public the rest are "hiddenish". They should show up if you click on show global acievements. The hiddenish achievements do not have descriptions as to how you achieve them.

Have fun playing the game!

Hi suspectDevice12, and thank you very much for your reply! Very useful.
I just have one more question about the point 1).
I still don't understand how I can get get 3 medals if every time that a round ends, everything restarts from scratch from the "select character" screen (hence resetting the medals count too).
Is this a 8 players-only feature? I only tried the 4 players mode.

The game isn't over when the title screen is displayed, that is the end of a round. For the game to really be over you need to press "esc" at the title screen. This will take you back to the main menu. Medals are available in 4 and 8 player modes.

Medals for 8 players mode doesn't work. I want to use this for an event but without medals it's not as fun.

Also I think this game should be posted to itch.io for more to enjoy since it's been removed from Steam Store. Great game concept!