I agree, most inverters make a humming noise, usually more hum the bigger the inverter.
As mentioned, no need to worry about the water heater. Don't drain it all camping season and it will always have water in it even if the fresh water tank empties.
Your last question is a "maybe". Make sure the wire running to the +12 connection on your Bargeman (7 pin connector) is at least 10 gauge wire, and understand that if you run your fridge on 12 volt mode it will use about 10 amps by itself - a large load. I usually use the gas mode on the road, partly so this load isn't present on the charge line. Also some TVs will automatically increase the voltage from the alternator when in tow mode to help put more amps into the camper battery.