Troubleshoot microwave, dometic refer and a/c

I don't have either the A/C or microwave so cannot comment.

Concerning the RM 8501 refer:  Are you able to run it on either 120 or propane?  In other words if you press the button for propane do you hear the ignitor clicking or when the electric button is pressed do you know if it is actually cooling even though the light doesn't light on the button?  If the ignitor clicks and gas comes on that is a good thing.  Same goes for the 120 side.  After 30 minutes or so you should be able to feel warmth on the cooling stack with your bare hand.  Also after 5 minutes or so you should be able to feel the heat escape from the black chimney stack.  At least this is a starting point.