Can I train my rabbit to not poop on my bed?

Short answer - no. Rabbits don't only poop when they need to go. They also do it to mark boundaries and territory, and this is not something you can train out of them - it's bunny instinct. It's probably a little risky to have him loose at night or when you can't watch him. You won't know what he's chewing or getting into. I never let my bunnies out in the house without being supervised, just for safety's sake, and because sometimes they can damage things you don't want damaged!