I'm sorry you are having a difficult time at the moment. I think, unless you pay rent to your parent, that you do need to do chores to make up the difference, pay for the roof over your head and food. Since it is your parents house, too, they can say who they like or don't like in their house.

I left home because my stepmother called me "stupid" one time too many. Were I you, I would make sure I spend most of my available time somewhere else, at school or a library
where I can study, search/apply for jobs or make plans.

I would tell your bf your parents don't want any of your friends to come to the house. You do not have to make it personal, do not tell him your parents do not like him, just that you are not allowed to have people over to their house. I don't think he will mind; the two of you can work toward after you finish school, have your degree and a job, and can get a place of your own.