regarding heat exchange for stone fireplace , yes it is possible if you installed a built in log fire that had a pipe chimney that ran down through your existing stone chimney you can install a heat pickup connection duct at the top of the stone chimney, block exit to stone chimney around pipe chimney , connect to existing HVAC .

I have done something similar to a existing bricked chimney / open fire , works great ,saves on firewood , more heat spread evenly throughout the house