Does the game have to be native or does it work through Proton?

Haven't tried any native games. Proton works depending on the game. For example Cyperpunk 2077 works but RT in Witcher 3 doesn't yet work (for me).

Is the performance comparable? Better? Worse?

Compared to Windows? Performance is worse but not by that much (for me on Nvidia). Depending on the game it is comparable. RT is very heavy on performance. You are going to want to enable DLSS or FSR.

Is it only working for AMD? Only for Nvidia? Both? (Neither?)

From what I've read they both work.

As already mentioned in another post it can be hit or miss. I think it works in most games by now. When Cyberpunk 2077 came out it took a long time for RT to work on Linux. Now it just works on most games I've tried. Witcher 3 being the exception since the update that introduced RT functionality. I'm on Nvidia. AMD should also work now. But supposedly performance isn't great on AMD (just correct me if I'm wrong).