It should not be possible to fully drain your water tank unless you use the drain valve and tilt the unit. The lowest the water can go is the bottom of the cold water pipe. Notice the blue line I added to the image.
However if your heater is still heating then it could evaporate all of the water and cause premature death for your water heater. Notice both heating elements are above the minimum water line so you don't even need to drain all the water to kill your heating elements.
It would be wise to turn off your heater until utilities have been restored. There is no sense in wasting electricity to heat water which you cannot use especially during rolling blackouts.
Depending on how long you have stagnant water in your water heater then you should cycle out 50 gallons of water through your tank once services are restored or else you risk exposing yourself to legionnaires disease among other things. Before cycling out the water bring the temperature up to at least 140°F for a few hours, cycle the water out, and then bring the temperature back down.
I am not sure what you mean by "heard it running" but it could have been air passing through it via your aforementioned faucet suction.
If you can then turn off your main water supply line to prevent the backflow symptoms. If the water supply returns while you're not home then it could be catastrophic if you had an undetected pipe burst or if your home is below freezing temperature. Once water has been restored then slowly turn on your main supply and listen for potential leaks.