I go from fad to fad, wanting a gf (never had one) to wanting to be cool and all that but all I want to do is have my own place, chill and a friend I can finally trust.
Sorry I just wanted to get this of my chest....
No need for apologies here,
Britishlad 
This is the place to get these types of things off your chest!
It sounds like your upbringing could have been more forgiving. Have you addressed your father's abuse and your mother's insults with each of your parents or any type of professional with whom you wouldn't mind divulging all the necessary details? As far as confronting your parents, if you haven't already done it, that could lead to high tensions and miserable conversations. Conversely, it could be that by doing so, you may bridge this gap that has formed between you and your parents that could be contributing to your struggle to accept your identity.
From the lines I quoted, I gather you may feel like you are a loner? (Please correct me if I am wrong!)
I know, like,
too many people who have felt at one point in their lives precisely the same way. I was a "loner" (though I was too naive and prideful to consider myself one!) from ages 14 until 22. They were lonely years, but years that, looking back, were really good formative years. I had a good time, and I got to "shop around" various social scenes and styles. I now know what I like, and, more importantly, what I
don't like. Perhaps you feel the same way. Nonetheless, it's still no fun to feel as though you don't fit in anywhere.
I always had this concept in my head that by age 18 or 21, one ought to have a firm grip on who they are and where they want to go. I'm 25 now, and my perception of myself and my role and place in this world is still shifting and evolving.
You're just about twenty years old. You don't feel as though you've got a firm sense-of self. That's
okay. The hardest part of the whole process of being
unsure is
reassuring ourselves that we'll each get there. There are so many differences between human beings; arguably more than there are similarities. Why would the timeline of comfortably adjusting oneself within society be any different?
Thanks for sharing your thoughts with us!
~ vaya