I would say to separate the issues because this sounds like a jumbled mess. You want to apologize for a few things (being possesive over him, snooping his room, ect) but you also want to stand your ground about who you are--a gay man--so if you don't feel comfortable talking to him in person, send him an email and state that you realize that you have made a lot of mistakes and apologize for those mistakes.
Then clarify the situations that he has misinterpreted. For instance, he feels that you became his friend with ulterior motives. Tell him this is not true. Tell him that your attraction grew from friendship and that's it.
Affirm to him that you are who you are and you can't change that, you do apologize for your mistakes, and that you do value your friendship with him and want to maintain that.
At the same time, I'd also add a few lines about how you can guarantee him that you will respect his space, his life, and his privacy in the future. The fact of the matter is that he is not in a position to trust you because you did basically break that trust when you snooped in his room. So, why should he trust you again?
You're human, you make mistakes, but you are hopefully recognizing those mistakes, and wanting to make up for them in some way because what you value the most right now from this person is his friendship.
Remind him how important that is to you, and then give him time to absorb it all and get back to you. Don't push too much, don't get too overly emotional. Just clarify things, apologize, and be as open and honest about how this situation got to this breaking point.
And that, IMO, is all you can do. From there on, the ball is in his court and he may desire to keep the friendship or not, but the choice will be his.
Well, I wish you the best of luck!