Various floor types over concrete slab

I'm currently renovating the down stairs of my house. It is 200 years old and has very low ceiling (about 7 foot).
The downstairs of the house consists of two living rooms, a dining room and a kitchen. All the floors are bare concrete with the kitchen and dining room having had a floor leveling compound put on them to level the floor. There are no pipes or wires in the floors.
The floor is slightly below grade (1 inch). SWMBO has decreed the following - Kitchen floor - slate tiles with under floor heating Dining room - that wicker carpet stuff, I think it is called seagrass Living room 1 - Carpet Living room 2 - real wood floor (with underfloor heating)
Previously the kitchen tiles were so cold in winter the bottom of my feet would go numb standing on them even with socks on. The living room carpet became stained (mouldy) in areas where furniture put pressure on the carpet.
So my considerations are - I need something that will insulate the floor and prevent damp coming through but be so thin as to not raise the floor level by too much. I was thinking along the lines of super proofing all the floors then laying 6 or 10 mil plywood throughout (except where the underfloor heating would go - I would get either 6 or 10 mil heating insulation board. I really need to avoid battoning the floor - I just don't have the headroom. Also I really can't afford to excavate the concrete floor.
So questions...
Would this set up give me the desired result (i.e. solid floor, well insulate, damp proof and thin)? Is super proofing a good idea or would laying something like 6mil polythene be better? How would I attach the ply without compromising the damp proof membrane? (The insulation board is supposed to be attached with a flexible tile grout). Is ply under carpet or seagrass a good idea? The solid wood floor will be just below grade level - is this ok? I have heard solid wood below grade is not advisable. I've heard sea grass is supposed to be glued to the subfloor, is ply ok for this? I heard talk of a vapour barrier - is this the same as a damp proof membrane? Finally - is 6 mil board solid enough for all the above floor finishes or do I need to go thicker? (10 mil, 18 mil, etc?)
Thanks so much in advance.

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