I believe you can, considering Xbox has the ability to interface with Windows through transferring save files. I'm not sure if you can modify those save files, but google can help you out with that

modifying a save file is not the same as a mod to change game and script mechices
witch is what the mod do via a creatin kit or geck

You have to have 2 Xbox's. Not worth it to me; I would rather buy a new PC.

Of course I would do almost anything to destroy the Letrush gang.

Yes you can, but you'd have to keep your xbox offline from then on.

Awhile back when I played a bit of ModernWarfare2 I actually joined a few modded public games by mistake.

Guns were shooting exploding cars and insanely crazy stuff like that.

An xbox would barely be able to run a lot of the mods that PC's can...

depinds on how much RAM the box has....
These mod will eat up the ram on pc