Singing

To me, they are both correct. I am a native speaker, but not a teacher.

Both are grammatically correct, but the meaning is different. If you say 'I often hear him sing in the music room', this means that you hear this from start to finish. The implication may be that this is done on some kind of formal basis. It suggests that you are perhaps a music tutor, and it is a requirement of a student's course that you have to hear him sing for an hour a day, for example. 'I often hear him singing in the music room' could mean that you simply walk past the music room and hear a few snatches of song through the door, or that his singing is audible from whatever room you are in. You don't necessarily hear the whole performance. The second is much more common than the first.

Su.Ki. Is correct, as usual