Welcome to the forum!
Sorry to hear that you are experiencing problems with your new camper and so far away from the selling dealer. Was there any discussion with the selling dealer in regards to warranty work?
The A/C unit should have the manufacturer's warranty in place. You could try to contact them in the UK...is it a Dometic or Coleman A/C? When you say that it trips out, are you meaning the 120V breaker for the A/C unit in the power control panel?
The bathroom light sounds very much like a loose connection in the wiring. Can you look behind the light fixture for that...if all's good there, check for a loose connection at the switch.
Nights camped in 2013 - 55, 2014 - 105, 2015 - 63