Could be a few things, the house being cold, a broken temp sensor, disconnect between the sensor and the furnace/pump.
You must have a heat pump with electric auxilliary heat.
I guess it's always running so when you turn it on you don't have to wait for it to heat up because its still warm, unlike when you turn the heat on in a car and cold air comes out and you have to wait for it to heat up. :(
As long as the engine is running, it is normal for the fuel pump to run constantly.
not sure of your application but possibly the pump on the boiler is set to run continuously and the thermostat energises the boiler itself.
You will have a flood PLUS your furnace will rust out. Can you hear it run? what happens when you fill the pump with water? Is there electric power to the pump?
depending on conditions but generally a heat pump will cost you less to run.
Yes, the outside unit of a heat pump system is supposed to run when the heat is on.
you can leave your furnace fan run continuos, it helps even the heat in the house, it also helps with condensation on windows.
No. The heat pump (your outdoor unit) and indoor blower motor will run ok at these power levels, but here is the bad news - if the heat pump can't meet the temperature demand (or it gets below ~ 20F outside), the furnace will attempt to turn on several electric strip heaters (as emergency backup). These strip heaters are rated from ~ 5000W to 20000W, depending on the size of your home. Your generator can't handle that load.
The fan should run for about 3-5 minutes after the furnace shuts off to help distribute the remaining heat throughout the house.
the heat pump is cheaper but the pump does not work as well when its below 40 out side thats when you want to run heat strip
No different than any other house. Heat ducts can be put into the slab when it is poured or they can be run through the attic and walls and a forced air furnace is used. Wall furnace, baseboard heat or they could have radiant heat in the floor.