Does the furnace run ONLY on gas ? And same with the WH ?

The thing to remember here is that the control electronics in the water heater and in the refrigerator while they are running on propane draw very little power. On an RV with a pair of deep cycle house batteries, the refrigerator can probably run for a week or more on propane without depleting the batteries, however the propane furnace blower fan could drain those same battery down over just one cold night.