I'm fixated on a girl that doesn't care to even know I exist
I'm concerned about why you would obsess about this girl?
I just really think she is a great person and very gorgeous.
Admiring someone you don't think knows you exist is fine if it doesn't get out of hand. Having a stable relationship with another person who loves you as you love them is more satisfying, find someone who can be your equal in that and many other ways. Otherwise you will be let down time after time.
It's fine. I can't expect that person to love me. I just want to give them a rough time and make their life a living hell.
If that is your goal I feel like it is wrong for you to have a relationship with her and I hope you think twice about making her life a living hell. It's wrong to cause violence against someone and it will not be okay for you to treat her that way the same way her ex-boyfriend has treated her and she deserves someone who will love her and care for her.