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To some of your questions:
Pipe material is typically polyurethane or PEX (cross-linked polyethylene);
Water will not be considered potable - will not be used for showers, etc.
The main drawback for the 'geothermal' approach is the length of pipe required - order of magnitude is 500 meters. Even with looping, trenching is extensive, plus the authorities require a certain displacement between the trenches - I think about two meters. So - it takes a fair amount of "yard" to accomodate. In new construction, though, the trenches could be cut under driveways or even foundations, but best not spring a leak.
As to the usefulness or effectiveness of this approach - it is proven by many installations to be one of the most energy-efficient systems for space heating in terms of energy used to run the system.
Sven notes below the 'trombe' approach. Definitely a good way to go. In fact my "pads" may need something equivalent to glazing to work well in my environment. Only possible advantages that I can see for the water-based system is the relative energy-density of water vs. air; the light weight and low cost of the "pads"; and the relative precision and ease of control of a heat pump via thermostatic switch. As I say, though, this is an experiment. Only one way to find out what works in my opinion.
As to Stirling engines - I have a sketch and some ideas on a related device. I intend to work on it concretely after retirement.
As to air exchange - I hadn't really thought much about it in the terms that you mention. Currently, there is some warm-air leakage via two bathroom vents, a fireplace chimney, and the clothes dryer vent. The heat exchanger for the heat pump is set in the middle of a finished basement. If I go to a heat-exchange mode of outside-air intake, I will have to construct some kind of pipe system. Sounds like a good idea, though.
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