Hot Water System

Hot water is leaking from the faucet even while the hot water knob is turned all the way off. It is an older system separate knobs for hot and cold water with the diverter in the middle that goes from left to right for tub to shower. I am assuming it may just be something like the washer or something similar needs replacing but where it is not dripping from the knob itself but the faucet I wanted to ask.

I’m purchasing a home with a incomplete baseboard hot water heating system. Most of the piping is in place, as is the heating unit itself.

I would like to replace the baseboard system with a force air system using convectors in each room. Since the convectors can be used for both heating and cooling is there an independent, stand alone cooling unit I can purchase to integrate with the present heating system?

And if you can provide the make and model number of this unit and that of a heat/cool convector it would be greatly appreciated.

My mother is concidering putting in the Hot water on Demand system. What would be the cost of this? Can someone give me some general information? Additional Information
-There are just two of us home, my mother and I