Welcome to the forum
What go size battery did the dealer install? If it’s a gp 24, it’s not going to make it through a night if you run the furnace. How many watts of solar?
Your Roof air is 120VAC only so it has no affect on the battery. Do not twist the handles for the dump valves, they will come apart if you do. You can turn them clockwise to make sure they are still connected, you should get some resistance when tight. They can be stiff to pull out/push in. Just use a little bit of force, if it doesn’t want to play ball then it’s time to call for warranty service.
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2012 Copper Canyon 273FWRET being towed by a 1994 Ford F350 CC,LB,Dually diesel.
Airlift 5000 bags, Prodigy brake control, 5 gauges on the pillar.Used to tow a '97 Jayco 323RKS.
Now an RVIA registered tech. Retired from Law enforcement in 2008 after 25+ yrs.