First thing, move back home. I know it sucks, even with parents you get along with, but situation dictates it's the best move. It'll cut your bills down something fierce. So talk to mom, get her okay, and move.
As for the job itself, you're fretting two things at once. You're fretting your job and school. As you said, you already missed the deadline for school registration, so there isn't much you can do about that, at this point. What does it take to get on the waiting list? Can you still get on it? If so, do it. If not, get all your paperwork ready and apply as soon as you can for next semester. Then it's out of sight, out of mind. Just worry about the job issue for a bit.
You know what? Some employments just aren't for some people. You may do well at a job in one place, but take that same job in a different company, and you can crash like the Hindenburg. You just need to write it off as an experience and move on. I know it's tough to do, but you can, in time.
One thing I can suggest; just worry about your own work. Don't bother with the gossip mills or who has it in for who. Looking through your post, you noted that you weren't given training, the facility was horrible, everyone hated you, your boss alleged that you sexually harassed someone, and no one (including you) liked your boss. I'm seeing a lot of blaming of others, here. I don't know how much is true and how much isn't, and frankly, I don't care. However, chances are that your perception does show from time to time at work; we can do a lot of things well, but burying our emotions isn't one of them. So valid or not, you may well come across with that "I'm better than all of you" image, and that doesn't help you any.
So try toning it down a bit. Just do your job, be nice to people, and don't get caught up in workplace drama. That's my thought, anyway.