No problem towing with the fridge--start it up about 2 days before you are ready to leave, then turn it off when you get home.
If you don't have a thermostat/temp control in the water heater, then you probably have the DSI (Direct Spark Ignition) model--as mentioned, there will be a switch somewhere and it should have a small red indicator with it.
2016 Tiffin 40 QBH
2015 38RSSA, traded
2005 TK3 #1869, 10 yrs of memories,
2017 F450 KR--one more Ford is it
2009 F450 4x4-died; 2010 F450-retired