Just like how they work on windows, you add files to the game directory
You might have to add a dll’s name in the wine prefix’s winecfg (or protoncfg)

It's explained in the link

You might want to try Heroic Games Launcher (for GOG and Epic) and native Steam in that case.

I've had a lot of trouble with Lutris, whereas installing and launching stuff from HGL and Steam works flawlessly every time.

Depends on the game.

There have actually been a few other discussions lately here about mods on Linux. You might check those out as well, but from what I understand, this linked one is very promising.

this isn't really a coherent question, mods don't work any specific way on any OS, it all depends on the game you're talking about.