A. This is a possibility.  Thanks to innovations in tecnology, such as the hyper-heating inverter, heat pumps can now keep a home toasty warm even if outdoor temperatures drop to 0^ºF!  That's a big improvement over the heat pumps of the past, which became ineffective when outdoor temperatures reached the freezing point (32ºF).

A. You can close some vents in unused areas of the home but be aware that your insulation is the exterior walls, if you let the room get too warm or cool you will still need to overcome that in the adjoining rooms. Closing off too many vents may also cause issues with the furnace or air conditioner.