If you put them on the playlist, then move them, they'll still be there and ready to listen to on the playlist ^^ Usually, I just put them on the playlist, then sort them to whatever folders I want.

If you remove the files from your computer, it's the same as if you had just put them in a different folder. They'll still play on the iPod and be there to listen to (on the iPod)

Hmm, the CT soundtrack problem is odd but it should be alright to upload, I'd think.