Lights dim, sound like a converter or battery problem. When is the last time the water was checked in the battery? The battery could also be pulling the converter down causing the fridge not to work, As for the AC, it is on it's own breaker, so check that. Not sure where the power for the thermostat comes from. You might also check the voltage at one of the outlets, just to make sure it is near 110 volts, not 90 or something low. If it is low, this could be all your problem, and may have damaged some stuff.
One last thing, unplug the power cord, and plug it back in a few times. If you are permanent, the plug may have corroded some, causing a low voltage condition in the camper.
2012 Ford F250 ext. Cab 4x4
2002 Jeep Wrangler Sahara
2008 Yamaha V-Star 650 Classic
2008 Work and Play 18LT