I know in True Any% that 2P is allowed, but I was wondering if there will be a category where you must use 2P and beat the game as fast as possible.

That probably won't become a category, but of course you can just do a 2p run for True Any%

Yeah, I guess

The mods should make it so that when you submit a run, you mark 2p "yes" or "no", so it shows on the leaderboard.

yeah, that would make a lot of sense