I turn off the water pump and water heater when not in use.....most of the time unless I forget, lol. Just in case of leak for the pump.
1 battery may be tough to stretch that long. However without a generator or hookups to charge, you could start your truck and then swap it into the truck to charge if necessary.
With no showers, that seems like enough water if you conserve. But if it's hot and you're using it for drinking water then that'll eat up a few gallons unless you live on beer. (That's my excuse, conserving water!)
Bring a bunch of tools. Especially if the camper is brand new, but either way, nothing sucks more than a problem that is easily fixable but you got no tools.