Not all heat pumps are air to air - it's usually air to water, so radiator loops for heat distribution around a building.

Erm, no. For an existing house you need to pay a one off fee to connect a solar installation to the grid - that is to confirm there line capacity for the amount you wish to export based on the local grid capacity, or the amount/rate you might want to store in batteries. After that there are different ways of connecting things up, including getting paid for surplus you export.

I never get the pride some parts of the US have in giving in to fear - if you feel you need to leave the house with a weapon, you are not winning at life, not in the slightest.