Safety has many sides. As far as fueling, the basic rule and law there is to be NO open flame near the fuel pumps. What that means as far as our trailers are concerned the
propane needs to be turned off when fueling.
Now as for running
fridge on
battery while traveling. I've done it a few times but never trusted the tow to keep the house
battery charge at the same time. I even have 150 amp alternator in my Dodge Dakota with full tow package. From experience the stuff in the
fridge doesn't get warm with the
fridge not running for a couple days in 90°+ high temps. If you're worried about it a couple of frozen water bottles put in the fridge before you leave home will do the trick and you'll have battery for
lights and
furnace when you get to your camp destination.