How do I win back her trust?

My girlfriend and I separated for a few months because she suspected me of being unfaithful. I admitted that I was and also accepted that she was right to break up with me. We got back together after a few months because we stayed in touch, and I was genuinely sorry for what I had done. The thing is, even after four months of being back together, she doesn’t always accept what I say. She questions me if I am away with friends, and I recently found out that she cross-checks my responses with them to see if I am telling the truth. This hurts me a lot because if she doesn’t have faith, how will our relationship survive? How can I get her to trust me again?
You can’t, until she arrives at that place on her own. What you can do is acknowledge that she is trying to come to terms with what has happened in her own way. Betrayal causes a lot of pain and can take a long time to heal. You admit that you hurt her, which also comes with the responsibility of being patient until she can move on from that grief. If she wants to verify your responses, it is simply her way of making sure your actions match your words. It is all she has to strengthen her belief in you, and you should wait until she gets to a point where she doesn’t feel the need to doubt you again. It is only if this behaviour continues for a prolonged period that you should have a conversation about it, if only to point out that forgiveness doesn’t work if it isn’t unconditional.

How do I know if a male friend of mine wants to be more than a friend? He keeps giving me hints but doesn’t say anything specific.
How do you feel about him and what would you like this relationship to be like? Nothing stops you from asking him a direct question to avoid any potential misunderstanding.