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..

Excuse my duh-ness but i'm having difficulty trying to follow whats going on here. Are these two photos an exact replica of your house and pool ? If not a hasty sketch with dimensions could help a lot. By kitchen wall do you mean the wall behind the bar ? And where is the pool wall ? Are you considering the covered area as being "inside" ? Sorry for all those questions lol Sometimes when you have a design problem you need to turn it inside out or on it's head. If you can't beat it maybe embrace it by making a feature of it : i.e. contrast by having the lightest colored pool surround and a great blue or tile inside and under the overhang, something that will echo the water color ? If you have a great covered area as in photo you'll most likely be spending a lot of time there and it could be soothing to be able to sometimes retire into a darker inside. In my book, 10M isn't small and also contrasting two floor colors doesn't necessarily make a space seem smaller and confined and may in fact even open it up. Could it be that you've thought yourself into a box here ? Sometimes one needs to give it all a good shake up and see how it resettles.

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.