You are generally fine with graphic and texture mods. Tyres, skins (including HD skins), steering wheels, helmets, track graphic mods (advertising hoardings, painted kerbs etc.), and force feedback mods.
There are a few protected files (I don't know them all), that prevent tyre grip mods, and database mods from being used. So if you have replaced your standard database.bin file with a modded one, you cannot play online.
If you have these mods installed you will be allowed to join the lobby, but you will be dropped once the session starts, with no warning telling you why you were dropped.
Personally I keep multiple copies of the F1 2013 folder, one standard default, one modded with a few graphic mods, and one loaded with mods than cannot be used online (hard drives are big and cheap nowadays). I keep the standard one on another drive, and the other two are all in my Steam install, and I just rename the folder(s) I want to swap in or out of the game.
You can use a mod manager software to individually swap mods in and out of the game on demand (search for Ryder Mod Manager) ........ too late I've done it for you
http://petar.outer-heaven.net/downloads/
If you want to get your game back to it's default state, removing your mods, just verify your game files via Steam.
If you don't know how to do that, have a read of my sticky here :-
http://www.racedepartment.com/forum...ntrollers-recommendations.73877/#post-1510267
Cheers