I need to explain how wrong I was...

I was wrong about something and ended up breaking my relationship by cheating on my partner. I know it was horrible, but it was based on a misunderstanding and there’s nothing I wouldn’t do to go back and fix things between us. He won’t take me back, and I understand that, but keep hoping that I can convey how mistaken I was. Maybe if he sees how genuinely remorseful I am, I may be able to turn things around and find a way back into his life. How do I do this?
You can’t force someone to come around to your point of view if they aren’t willing to communicate. Your remorse may be genuine, along with your desire to give this another chance, but it can’t happen without dialogue. All you can do is try and explain yourself in detail, email this person if he isn’t willing to meet, and hope that your explanation allows him to reconsider how he feels. He may need time to process this, because the end of a relationship inevitably causes pain, so try being patient and hope for the best. If he doesn’t reach out, you may have to simply accept the possibility of that conclusion too.

I’ve been friend-zoned by someone I really like, and I think it’s because she just cannot imagine a friend as her boyfriend. We have known each other from school, and I only recently began to develop romantic feelings for her, which makes it frustrating because I don’t know how to get her to see me differently. Should I tell her how I feel?
This is a friend, so you should be able to have that conversation without any awkwardness. She probably doesn’t see you as anything other than a friend simply because she hasn’t considered the possibility. However, you should make it clear that she doesn’t have to reciprocate, to avoid damaging your friendship. Be honest, tell her that you value her presence in your life, and be mature enough to accept her decision.