Welcome to the forum, and welcome to Airstreaming. I know you have lots of adventures ahead of you.
The airconditioner has a water drain tube that is supposed to take all the water to the outside, and normally shows up somewhere along the wheel well area. You can usually see the drain tube by removing the inside plastic cover. Like home airconditioners, sometimes that tube gets stopped up.
There is no fuse that I am aware of on the tail light circuit in the trailer. That would be fused in the tow vehicle. You should test at the seven pin connector, vehicle side, to prove the circuit to that point, and if you have voltage there, suspect the trailer side of the connector first.
Good luck with your fix-up.