I'm going to be parked in the same place for months. I was hoping to just utilize a direct line to the water. My question is, is there a valve that needs to be closed? The upper three from the top down are open, closed, open. What's the deal with the valve nearest the pump? Should it be on or off?
On the suction side of the pump, the side with the clear filter bowl, there's a tee for a short piece of tubing that has a valve. That is the antifreeze suction line used for winterizing. That valve needs to be closed, or the pump will just suck in air instead of water from the tank. But if you're not using the pump, it isn't relevant to your problem.
The water heater bypass positions sound right, and even if wrong, won't interfere with water flow. If wrong, all you get is cold water through all faucets.
The reason you should try pumping water out of the fresh tank is to isolate the problem location. If everything works when on pump, the problem is close to the water inlet where the hose is connected.
Another consideration is if you have low point drains. There is water in the tubing above the drain valves that's exposed to outside air. It'll freeze and the ice can wick up into the tees, blocking some of the water lines.
It sounds like you've got a blockage, possibly from ice, and you need to try some isolation tests to locate the blockage.