Hi and welcome.
What you describe is pretty stressful and so sad and difficult. I am sorry for what brings you here but I am glad you are reaching out for support here and through therapy.
I'm 21 but have never lived away from my parents, I've had separation anxiety I guess from worrying what is going to happen if I'm not there
I can very much relate to the anxiety and worry you express here. I felt the same and thought I was somehow helping things by staying with my parents. I did it for a much longer time though, not moving out until my late 30's. I get it. The thing is, this is your life and there is little you can do while in the midst of the disorder to help them, and what you can do is even limited when you are out.
I feel guilty for lying to my parents on the incomplete and am feeling like maybe I'm overreacting as 80% of the time my mom is loving and kind towards me but emotionally attacks my dad.
At your age, it is natural to separate and begin to live your own life. An 80/20 split is hard to deal with I think when there is such a contrast between the good and the bad times. It can be quite stressful and confusing as well.
Does your school counselor help you with coping strategies and managing your anxiety? How supportive is your father? We can help you here but sometimes it is good to have some face to face support as well.
Have you ever heard of the text line 741-741? It is a support line for anyone in a crisis. I am wondering if this could be another support reference for you to use when feeling anxiety about your move? It provides free 24/7 support and is pretty easy to use if you want to try it in addition to posting here. You do not have to deal with this alone.