Before you panic, check the obvious: Is the propane actually on? Sometimes the valve gets bumped accidentally. Also, make sure the fridge is set to propane mode, not electric. If those are good, it might be a simple sensor issue.
PVC's fine for that, but use a proper septic fitting, not just a glued-on cap. You'll want something designed for that kind of pressure and potential shifting of the ground. A concrete pad is a good idea for stability.
Dude, that's weird. .814v with shore power connected? Sounds like something's sucking the juice out of that battery while it's charging. My guess is a short somewhere, especially given the mouse damage. Even a tiny short can drain a LiFePO4 battery p...