My Xbox moves from my room to the living room all the time since my roommate's a pain in the ass about it. Almost all the time it has a disc in it, but it always turned off (at least it better be) when being moved. I take great care of my games and have not found any scratches on them yet.
Not sure what to say except try taking it to a game rental store and see if they can send in your game with their next batch to get scratches removed.
As far as noises, I do believe the Xbox is just a hell of a noisy beast. I actually folded up an area rug and put the Xbox on top of it to reduce vibrations from the disc spinning before I learned how to install them.
If you install the game, the disc will spin for a short time while starting up, then goes quite for the rest of the time you're playing.