No. FiveM is developed exclusively for the PC version of GTA V. There are no plans to support consoles.
The FiveM client cannot run on Linux due to no support for shared resources in DXVK. You can run a FiveM server on Linux.
That depends on how you installed it in the first place.
WinKey+Ron your keyboard
%localappdata%/FiveMin the dialog that opens
More about installing FiveM here.
Nope! As mentioned on fivem.net, FiveM does not interact with the Rockstar Online Services other than to validate your game copy the first time you launch it. This validation emulates the game's interaction, and can not be detected by Rockstar. It also doesn't modify your game files at all, even when downloading server assets, so you don't have to do anything to move between FiveM or GTA:O.
It's never fun to run into problems. Read the client issues manual for help.