Sorry your dad is depressed. The best thing you can do for him is to be there for him and sometimes that means just sitting with him and being there.
As far as you mom goes try to remember she's not the one irritating you. Try talking to her about it in a calm manner if at all possible about how you feel when her bf picks on you. School can be very anxiety prevoking. Do you have any friends from last year to help ease going back? Keep in touch with the friends you have and maybe that will ease the anxiety. Do you see a counselor? Maybe it would be a good idea if you don't. They could help teach you coping skills for you anxiety.
Good luck
Gayle