I worked on a long term research project where auditory processing was one of the elements looked at in one of the studies. I may have access to sources that are unavailable to you. In other words I should be able to find pertinent research information for you, if it has been done..
I would like if possible for you to clarify your question, since there seemd to be other questions specified beside just the two in the title. But if would just like me to find research results on auditory processing and related to handedness and auditory processing and music therapy, I will be pleased to look for this.
I do know of research that shows neurological pathway changes (and improvements) are possible due to neuroplasticity (the younger the individual the better) so I think it likely that music as well as any other activities where the pathways are used will bring improvement. For example, music therapy will likely help with auditory processing of music, but for auditory processing of speech, activities involving speech would be helpful.
The ability of your son's brain to change may depend somewhat on the nature of your son's disability. For example, was there ever any trauma to his brain? Has he ever had any studies of his brain? If so, what were the general results?
If you do not mind, Please answer the above as well as specify exactly if answering the two questions as I mentioned above are what you are requiring to be satisfied with your answer.
Additionally, I will be at work away from a computer this afternoon, but after getting a reply from you I can start to work on your answer this evening.