You can seal the wood with anything really. Paint, polyurethane, etc. I'd opt for a strong paint personally. If you go with a polyurethane, make sure it's UV rated.
As far as what to put over the wiring is gonna kind of be up to you. You can get some thin pieces of plywood from a home improvement store and cut them to be the size of what you are wanting to cover up.
Do you have a picture of your rabbit hut? That would help others give you ideas on what to do.