The majority of RV absorption fridges are two way, propane and 120V power (often with 12V controls for both power sources), and obviously won't run on just DC power. They do take a good length of time to cool down; I'd ask that the fridge have run for awhile before checking out the unit (overnight or at least several hours) and check that it's cold inside. Assuming the cooling unit is working and it's getting cold, verifying gas operation is pretty easy--is there a flame there--while electric might be a bit harder. The nice thing is that problems that affect only gas or electric operation are comparatively inexpensive to fix, at least when compared to a nonfunctional cooling unit.
A water heater on gas will heat the water up from ambient to full hot water temperature in maybe a half hour, fairly quickly. Then again, If there's fire heating the water--which is quite self-evident when its operating--it's basically impossible for it to not be heating the water. Electric operation could perhaps best be observed indirectly by seeing if power usage goes up when the element is turned on. I'm not sure how many truck campers would have electric elements in their water heaters, but doubtless at least a few do.
(Besides the air conditioner, don't forget about the furnace! I suppose that's a wee bit less of a concern in many parts of Arizona than it is here in Vermont.)
To a certain extent, buying a used (or new) RV does involve a little "you's pays yer monies, you's takes yer chances."
