Space Heating

Is an "Air source heat pump is used to heat hot water for" hot water baseboard heating. "Also has anyone put a" Sterling Engine "between the hot side and cold steel heat pump to generate power for the system?

The heat pumps used to heat sufficient to heat the water to a usable temperature.
Now, a liquid to liquid or air heat pump using a well or possibly a pond can function as an auxiliary system.
Mother Earth News has some articles about it.
A heat pump is in fact refrigeration system that can be reversed by pulling or more precisely the heat absorbing side of the evaporator. (Cooling side)
You can cool more efficiently with the well or pond set-up instead of collecting the heat from the pond or
I assume that sterling could work, probably the best in the closed loop system and freon gas expansion.

Both would be ineffective. A sterling engine is not much torque did not have enough power to make electricity enough to be a great help. As the hot air from a heat pump will be permanently heat water to make a difference in temperature. Water is denser than air, so it should be so much to operate.