Malconium, the most common denominator of the systems you list is the propane supply. I would start there, and ensure that is safe and legal. You need the tanks to be within their certified dates, fitted with OPD valves, and with recent rubber hoses without cracks. The regulator needs to be checked for 11 inches of pressure, and the whole system checked for leaks. Once you have a safe and legal propane supply, I suggest you light the stove and oven and repair any defects. The next could be the water heater, as that is probably only propane powered. Servicing this is not complicated, involving removal of soot, adjustment of the burner, and blowing sediment out of the tank with a water jet. If the heater then works, and the tank does not leak through corrosion holes, then all is O.K. The air heater should be serviced before use, as there may be obstruction of the vents by mud daubers, etc. Most people will leave this job to a qualified professional, and you could certainly disconnect the heater and take it to be serviced. Removal of the heater does, however, require confidence in disconnecting electrics and the gas line.The forum search facility will give details on how to service the other appliances. I suspect that, from the way you have put the question, your best bet would be to trail the coach to an experienced service agent for the systems to be checked. I would not recommend removal of the refrigerator or water heater, just for them to be checked. Have fun! Nick.
Nick Crowhurst, Excella 25 1988, Dodge Ram 2500 Cummins Diesel. England in summer, USA in winter.
"The price of freedom is eternal maintenance."