Not rambling at all. I moved this to the Podmod section. The pHp section is more for on-the-road-I-need-assistance.
Leaving the pump on should be fine. If you do and you hear it kick on every once in a while you have a small leak somewhere. Often it is the water heater overpressure valve that needs to be jiggled. We turn ours off at night partly to turn the light off, and also because as the water lines change temperature overnight it might kick on once briefly which can wake you up.
Water heater is also fine to leave on. With our popup I would always turn it off after our showers and dishes. We had enough hot water for hand washing the rest of the day. Then one day I spent the day near the water heater and forgot to turn it off, and barely heard it come on all day. Didn't bother turning it off after that. More trouble than the LP it might have saved. However, that was with a manual-ignition WH. Since it is so easy with the pods - one switch inside - it is up to you.
Yes, at home as part of de-winterization you should leave the hot water valve on until the sputtering stops. If you used water from the fresh tank to do that make sure to refill it because that will suck up 6 gallons - this also means you will have used the pump to fill the WH and that is find. If you used the city water connection then you are done. If the WH isn't full and you turn on the electric element it will instantly burn out. That may be what he meant.