I am so sorry you are going through this. You are very mature in your analysis and therefore may want to either enlist the help of your mother to play interference and help you avoid meals with your father. Your health is too important to jeopardize that. I had a similar situation in my youth and while he was not diagnosed as a psycho, actions spoke louder than words. I would literally make sure I would leave the house when he was in it, or at the very least leave the room. I found that if I had at least one "date night" with myself where I would figure out what helped calm me, life was easier. I always recommend that to friends and family alike. Whether it was putting on candles in my room and meditating, or reading a book and having a bath with candles; whatever worked, I knew I had to learn to unwind and relieve stress. I would suggest you do the same.
It may be an idea to let your dad know you need some time apart to sort through things. Perhaps you can get someone to talk to do get through this and help you set goals (i.e., one week without throwing up after a meal, etc...). Baby steps and accomplishments can help you move forward with less stress.
I realized at an early age that I would more or less become my own parent and I got great strength from pushing myself and setting goals, getting mentors of elders around me (teachers, bosses, etc.) who can help me focus on what is important.
When you are in school, your focus should be on education, not social, so social education can occur after school, if that important to your parents. If you feel you can focus best at home then perhaps work on that goal and help yourself heal. Perhaps join some school social activity during the week, so that can solve your mother's concern for social interaction. However, you can also advise her that you are there for an education and the social interaction can happen after school. Can't argue with that.
You will have down days, but do not let yourself stay down. Read motivational books, keep yourself positive. That is the only way you can get out of that funk. When I was young I realized the reason I was in an unhealthy environment was to learn from it and create a healthy life for myself. Perhaps you can do something similar? Stay positive! You are the BEST advocate for yourself!
Keep us posted!