Counter-strike works, as do all valve titles. Overwatch, Splitgate and Titanfall work as well and so do most "non-real-time games", like Trackmania. Riot's games and Rainbow don't work. Check protondb for the games that ate important to you.
I haven't had any such run-ins yet. When I asked them to replace my iPad's batteries, they said that they couldn't do it, but gave me a new iPad of the same model for CHF 100.- (which would have been the price of the battery replacement).