w/o/w: Again, speaking from experience, I would say there are 2 things that cannot coexist: helping your child and at the same time trying to hide him because of worrying about what the community will think. One thing for sure, our kids have sensitive antennas and if we are ashamed of them, they pick it up quickly and resent it. So as difficult as this step is, it is really step one: make your son the priority over your reputation in the neighborhood. And of course, this is where a support network would be invaluable, but I cannot tell you where to find one.
As for how he spends time, he may be content with laziness for the time being, but eventually he will probably realize that he can acquire things for himself if he works. It may be that the idea of work doesn’t occur to him, or he thinks there is no job he can do. I don’t necessarily think this is the correct path for him, it would be better if he could connect to someone who would turn him back on the derech.
It’s interesting how he is challenging you, by letting his sibs listen to the forbidden music and warning you that you have to support him until 18. Could it be that he is daring you to show strength and resolution? It does sound like he has an agenda of some sort, have you figured out what he really wants, other than a computer?
If the teasing/bullying is really the motivator here, it can be a rough road ahead. Been there.