Apologize sincerely. That's the first step. Tell her you know you made a huge mistake and that you're deeply sorry. Then, give her space to process her feelings. Don't pressure her to forgive you right away.
No, it's completely unethical. Being involved with your best friend's girlfriend goes against the principles of loyalty and respect in a friendship. It can cause a great deal of harm to your friend and damage the friendship irreparably.
I've heard of such stories before. In one case, the guy noticed his friend flirting with his girlfriend at parties. He was really angry but didn't know what to do at first. He decided to show more affection to his girlfriend in front of his friend. And he also had a private talk with his girlfriend about their relationship boundaries. His girlfriend then made it clear to the friend that she was only interested in her boyfriend. It's crucial to be assertive in such situations.
Well, it's a really difficult situation. You should think about what you value more in a relationship. If loyalty is very important to you, then it might be hard to continue with your girlfriend. Regarding your friend, this is a serious betrayal. You can confront him and ask for an explanation. But keep in mind, whatever you decide, it should be for your own well - being. You don't want to be in a relationship or friendship that makes you constantly feel bad.
Tell her how sorry you are right away. Listen to her feelings without interrupting. Maybe offer to do all her chores for a week or something like that. Also, show her that you trust her by giving her more access to your own private things. It'll take time to make it up, but being sincere is key.