Yes, you can run both at the same time it heats up very quickly this way and recovers faster too. I only run both at the same time during showers and hot never runs out for us. Yes, you can leave them on all the time, except when towing. If at a place with full hookups I would just use the electric side and save your gas though. You could trip your breakers if running the electric and a/c the same time if you run the microwave too.
2015 GMC Sierra 1500 Crew Cab Z71 4X4 3.42
2013 CrossRoads Sunset Trail Super Lite 250RB