Yes. There is an entire field of music therapy, and a large amount of information about this can be found on the internet. As they say, music soothes the savage beast.
Most definitely. Music has been associated with healing since ancient times. Rather than being a curative for specific conditions, the powerful effects of music are general and facilitative of, e.g., desired mood states and memory retrieval. Creating and listening to music are complex activities integrating many parts of the central nervous system. "Without music, life would be a mistake." Nietzsche.
Indirect. Music can be comforting, relaxing and remind you of times in your life when you were feeling well. It can thus promote well being and this may contribute to healing to some degree. It can be a useful adjunct but not a treatment in itself.