Water – How does the geothermal heat pump heat the hot water tank/UV filter and softner

I've been looking into a heat pump replacement.
You said "However, when the heat pump is in heating mode, the exiting refrigerant line is actually colder, not hotter, than when it enters. As a result, you cannot heat water during the winter."

That will depend on the location of the internal connections. The HP models I have seen with a desuperheater ( hot water generator ) place the HWG after the compressor before the reversing valve. That means the pump always runs forward, the HWG always has hot refrigerant to use and it works in summer and in winter. The reversing valve does just that - in summer it sends the leftover heat to the outside and extracts heat (cools) the inside. In winter it sends the heat to the inside and extracts heat from the outside.

It can backflow if you lose pressure. Perhaps from a power outage, or if you draw water faster than the pump can replenish it.

Backflow valves (check valves) are pretty cheap (about $5 - $10). If the consequences are as severe as you make them out to be, I'd put one in.

Also I would add a carbon filter after the RO system, that would remove ammonia and other things, just in case. If the water was clean the filter would not get worn, so it's cheap insurance that you can leave there for a long time without replacing the filter.

PS. It's good you are not trying to drink softened water - the extra salt is not good for you.