See your badge page for "card drops remaining". Free games don't drop cards unless you spend a lot of money on DLCs or micro-transactions.

I didn't get cards for 112 Operator, Ballistic Overkill, Rainbow Six Siege, CS:GO and stuff like that, even when I payed for most of them

And for some reason it says no card drops remaining

IM doesn't give you cards, Steam gives you the cards - once only per non-free game. If steam says no card drops remaining then it won't give you card drops.

Steam says you've played Rainbow Six Siege and CS:GO etc for many hours in which case you would of already have had the card drops for those games.