Could "Lips" for Xbox 360 be effectively used to rehearse a song?
Yes, Lips keeps track of the score of the imported song you're playing, it detects the pitch and tells you how well are you doing it. I'm not sure if it works correct on 100% of the cases, but overall it seems to do a good job.
I don't do singing, so i couldn't tell you if it works fine to practice your singing skills.
Yes, the game do vocal reduction but I don't remember if you can adjust the level of the reduction.