To determine if a propane tank that doesn't have a gauge is empty, you'll have to lift or weigh it. If the tank is in use, you should notice the lower part (where the propane level is at) will be colder or even have condensation on the outside. Thumping will work if you can tell the difference.
If you're connected to shore power, then the frig will automatically run on 120 volt. If you're not connected (or the breaker is tripped) then the frig will try and work on propane. If you're out of propane, then the frig will give you a flashing signal that it isn't working.
If the breaker flipped on the air conditioner, it could be due to low voltage which could be caused by excessive electrical demand from the post.
Turn the power off at the post. Turn the air conditioner off. Turn the frig off. Turn the water heater off. Turn the power at the post back on. Turn the air conditioner back on. Turn the frig back on. If one of the circuit breakers trips, you are drawing too much electricity and will have to turn something off.