Hello and welcome. I will address the refrigerator. You say you have lights but the refrigerator will not come on. I am assuming that you have a camper refrigerator and they work different then the one at home. The one at home makes cold air the one in the camper is a heat absorption unit meaning it takes out heat leaving cold. If you are on electric and turn it on you will not hear any sound as there is a heating element in the back that heats up so it is quiet.
If on gas you need to be plugged in to 110 for the converter to provide 12 volts or have a good battery for the source of 12 volts if not hooked up to 110. The 12 volts provides a source of ignition for the gas and also for the control board.
The other thing to remember is that it may take over night for it to cool down. We turn ours on the day before the wife loads it a couple days before a trip. Now some people leave theirs on all the time but we do not camp every weekend so we do not.
Just Google " how does a rv refrigerator work" And it will explain it.
Another thought a 15 amp is pushing it to run the ac let alone anything along with it.
2005 Cruiser 29CK
2008 GMC 2500hd 4x4
Crew cab Long bed 6.0 gas
4.10 gear ratio