Pictures of your dining room and kitchen would be helpful.

If you are seeking a truly open feel to the floor plan you have shared, then using one material in the mail living area is the best approach to making this space feel truly open. Using a variety of materials on flooring chops up the space and decreases the visual footprint. I would suggest using wood, tile, or if you are on a tight budget laminated flooring for the living/dining/kitchen. Then use carpet in the more intimate spaces; bedrooms and possibly hallway. Save the tile for the bathrooms.

those tiles from the 1800s are encaustic... the color goes all the way through. ceramic tiles are red in the middle and have just a relatively thin layer of color and glaze. porcelain tiles do have a color matched center (look at the edges to tell) but i'm not certain that all of the pattern goes through. at least it would wear off and turn the main color, not red.

I cant imagine that tiles on concrete will be any colder than concrete alone. But the choice of colour may make a difference to the heat absorption qualities; dark tiles will absorb heat better than light coloured ones.