I suggest looking at one problem at a time to avoid info overload!
The water has a few easier things, so let's look there first. One is the way to use the pump. When not connected to water turn it on and it should then run for a bit to build pressure and then shut down until you use some water and the pressure drops so that the pump comes on again.
Leave it off when connected to water supply as you don't need both.
You probably have a fresh water fill port or there may be a valve to change from filling the tank to using the water direct, so if you have a valve, be sure to change it to the right "normal" position when done filling the tank---or your pump will not be able to pump up pressure!
The water heater sounds like it has a bypass valve setup that is left in the wrong position so that water is going past the heater, not into it to be heated. Don't run the heater while dry to avoid possible damage!
Try finding the bypass valve setup on the back of the water heater. one or two valves that turn to align the handle with the direction you want the water to flow. You can usually see a pipe that goes into the heater and you want the water to go in there and there may be other valves where it needs to come out. You will get water at the faucet the same but once you get it right the water will heat up pretty quick. Not unusual for the heater to have to fire a couple times to get it right after one has set for a while. Just need to get the water and fire together?
The battery charge process is a whole confusing ball of wax but not that difficult once we understand the setup. Are you familiar with solenoids? There is a big solenoid near the batteries and it does two things.
You likely have a switch on the dash which might be labeled AUX or boost. It is a momentary switch when held to the right position, it connects the start and coach batteries together to give the start battery a "boost" if needed to start.
But it also works to connect them when the engine is running to get the alternator to do some charge on the coach battery while we drive.
So to tell if things are working, this drawing shows a small wire that comes down from the dash switch, runs through the solenoid coil and gets to ground through the solenoid body to wire FM. When there is battery on LR, it makes the coil inside the solenoid move the contacts to connect the big cables on right and left side together!
One way to know it is getting the signal is to have somebody push the boost/aux switch while you feel for the solenoid to "clunk" as the contacts move. It should also do it when you start the engine but it's a little harder to hear/feel it when all the engine noise is going on.
But if the solenoid is closing but the left and right are not connecting together, the contacts inside the solenoid may be burned/ corroded too much and need replaced.
Sorry about the double post, that little bird called me to dinner and I lost my mind!