It probably sat idling a lot at the dealer. If they did not reset your MPG display when they filled the tank, you're still seeing the results of that. Figure out how to reset the display (depends on whether you have the Navigation system or not) and then see how it goes.

Also you can expect mileage will improve with age, things seem to get better after about 5000 miles.

Don't worry about when the gas engine is on or off...just drive with as light a foot as you can safely get away with in traffic, and you'll do fine. The best economy doesn't occur when you stay in EV mode all the time, as sooner or later you have to replenish the battery charge.

Oh, and the guess gauge is not terribly linear, so the odds are you have actually used less than 1/2 a tank...