Is it fair of me to ask her to delete it?
Yes, it is imo.
Is it fair that I asked to see her do it?
Nope. Trust her or don't.
Would it be fair to ask to see her profile and see the messages and conversations shes had on that website? (I feel this one might be too controlling)
Nope. Don't get into her business like that. It'll just lead to more drama.
How do I learn to trust her again?
You probably don't. She said she wouldn't do it again, then she did it again and made an excuse for why it wasn't as bad this time as last.
Am I making a mistake by staying with her?
Probably. Definitely try to define why you wish to stay with her. Be honest with yourself. Gf must surely be aware at this point that she's jeopardizing this relationship. Perhaps she feels that her needs aren't being met in some way. Have you asked her why she keeps doing this instead of trying to fulfill her fantasies with her BF?
Pain is what the world does to you, suffering is what you do to yourself. Pain is inevitable, suffering is optional.