I would not try someone who's income depends on making sales. High gloss floor tiles especially for bathrooms are not ideal since they lack grip once they get wet or when the bathroom is moist after a shower.

First be okay with the fact the bathroom tiles might need to be replaced. All of them. Replacing them in the bathroom will have the least impact on the rest of the house and whatever comes out in one piece, can be stored for future cracks. Maybe you can find a similar color but a different size, so it won't look too awkward, just an idea. Taking out a cracked tile is quite easy. Put on some gloves and safety glasses and (carefully) smash the broken tile with a hammer. An old screwdriver or chisel will help you tilt the pieces out. Work from the hole outwards to remove the other tiles. Removing a good tile is nearly impossible. Assuming it is still glued firmly, I'd say impossible. But, if you want to try anyway, you'll need to mill out the grout and then figure out a way to lift the tile..

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.