I hear you Papason:
I share your feelings too. It always costs too much and seldom is done correctly; I have had to do too much of their work after they have been paid.
Air to air heat pumps work best around 35* to 40* outdoor temperature. Their effieciency curve takes a nose dive when the air temp goes below 35*, and when it hits 17* there ain't nothin happening. That's when the resistance electric heat kicks on to keep you warm. The humming/buzzing sound may be an electric heating element for defrosting. Many units use a burst of hot gasses to defrost; either one costs you unnecessary money. I have seen outdoor units that looked like a big hunk of ice from the street and were still trying to work. About every hour they sound like a truck tire has been punctured (the rush of hot gas), then they start to trying to pump again.
A supplemental heater in the house will do a bang up job for you. A wood stove would cut your heat bill considerably if you could get free wood to burn in it. Or a wood fired boiler out back would be good.