If I was building something like this I would keep the freezer out of the root celler because the freezer is a source of heat, sure you can collect that heat and shuffle it around but the best option is just to put it closer to where you want the heat and where you want to use the freezer.
As for partition walls, is there an issue with using pressure treated wood with foam insulation? mineral wool insulation is ok below grade as well, not everyone is ok with the chemicals but once the walls are sealed up it shouldn't be an issue and pressure treated wood is still sometimes used to make wood foundations on houses, not my first choice but it works.
As for the cooling of the root ceiler rooms, it sounds like you have some complex ideas and I have to wonder if just using a window A/C unit might be the best rout to go, having it pump heat in to the warmer side of the basement, with a good thermostat you more or less end up with a walk in cooler built in to the house.
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