As long as you keep the heating strips from turning on in the heat pump, it is the most cost effective. Usually, there is a little indicator on the thermostat to tell you when the heat strips turn on. The only way to keep them off on some units is to keep the inside temp setting low enough to keep the chill off in really cold conditions.
To answer a few of the questions
1) A heat pump is like turning a window AC around. During the summer you notice the hot air that blows off the outside. Turned around it blows inside
2) The efficiency of the Heat pump is dependent on SEER. Like MPG the higher the better. I bet your existing is a 10 SEER
3) The Geothermal systems use ground water instead of outside air. It is like the outside air is always 50 deg. Not too far to heat or cool
4) Insulate, insulate insulate. Keeping what heat you have inside is the cheapest.
When your AC Heat pump comes on unless you have more than one thermostat it heats/ cools the entire house. Electric heat is not that efficient but a smaller heater in a room will cost less than the heat pump for whole house.