1. Wow, he's studying nuclear science? Dude, this is so damn awesome. Not many people get into nuclear physics. And he wants to give up on that for... what? Computer game development? Seriously? He has an option to do something that might change the future of the planet as we know it, and he would rather make games?
I'd tell him not to waste such an amazing opportunity. If he decides that this incredible sector is really not good for him, he can always switch fields later. It's easier to start with nuclear physics and switch to game dev than start with game dev and switch to nuclear physics.
Then again, in the end it's his decision. If he
really wants to do something else I suppose there's no point dedicating years of his life to study something that doesn't bring him satisfaction or happiness. I just hope he doesn't regret the decision.
2. Holy crap, his mom sounds like a control freak and a pretty terrible human being. Maybe he should get the hell away from her? Getting out of a toxic, abusive relationship is very hard, but if he decides to try it please offer him the support he deserves. Then again you can't really help a person who doesn't want to be helped, so it needs to be his decision. Talk to him about it? Tell him that his relationship with his mom is definitely not healthy and that if he does nothing about it it might end up destroying him? Read some sites about providing help and care for victims of abusive relationships (
http://womenshealth.gov/violence-agains ... bused.html and
http://www.helpguide.org/mental/domesti ... ention.htm come to mind).
3. If nobody likes him then it's no wonder he doesn't have a girlfriend. Who would want to date an unlikable person? Then again you make it sound like this person has a lot of issues that might impact the way they act around other people.
4. If he is depressed, perhaps revoking his firearms license would be for the best. I mean, mentally unstable people + potentially lethal weapons = a tragedy waiting to happen. Try to suggest some other hobbies to him? Perhaps something to do with fitness and sports? My suggestion would be weightlifting since it can help improve the mood, reinforce body image and in the long run you only compete against yourself and your own flaws, so it's great for building character when you eventually overcome them. (edit: just make sure to tell him to stay away from Planet Fitness. It's a horrible anti-gym which keeps people from getting any real exercise. You can get kicked out for lifting weights in there, wtf.)
I'm really sorry to hear about your friend's issues. I sincerely hope you can help him. Disclaimer: I'm not a doctor, so take everything I say with a grain of salt. I think it would be best if you could convince your friend to see a therapist, since a medical professional is always going to offer better advice than a random person from a gaming site. Good luck!