Took me a while to figure this out also. The switch inside controls ONLY the propane for the water heater. The switch on the heater itself when turned on runs the heater only when plugged into hydro. You can have them both turned on if you are on electric hookup and have the propane running also to make it heat faster.
So, if you are plugged in, as you say, you need to flip the little switch on the heater itself ( bottom left side of heater kind of hidden under other stuff). That will make it run on electric. I just leave it turned on all season. If I want it to heat faster or am not hooked up to electric, then I turn on the switch at the panel also and it will use the propane, as well. On electric only it does take a while to heat up.
If you leave the switch on at the heater, be sure to turn it off when you winterize. If the electric element is tured on without any water in the heater you will fry the element in a few moments.
Do you have propane to your stove working? Not sure what the alarm would be. It seems odd. Good luck!
Tina & Ted & pooches
2012 Ford F-150 XLT 5.0L V8 4x4 with tow package
Andersen WD hitch with sway prevention
2012 Rockwood UltraLite 2304s trailer