You can get them to work by enabling hyper-v inside the windows vm, but this kneecaps your cpu performance unfortunately. Might not always be an issue though depending on how powerful your cpu is and how demanding the actual game is.

Some of them will. It depends on which rootkit is used. There are some VM optimizations that applications can detect, but those can be disabled.

Most of them run in proton natively on Linux, but it does depend on the specific anticheat.

You can check protondb to verify how well a game might work on Linux

Personally, I boycott any game that comes with kernel level rootkits.