RV fridge not getting cold on propane, but freezer works?

Since the fridge works on electric power, the cooling unit is functional, and so the problem must be something with the propane burner or associated bits. My guess is something needs cleaning or adjusting in the burner.

The air conditioner problem is entirely unrelated. You have a broken air conditioner (or maybe a broken wire from the thermostat, but that's not too likely), but you already know that much.