^^^Jan's on it^^^ These aren't tiles they are stones. Real stones. A stone mason will help with the installation. A small install (kitchen only) can be dealt with by a tiling expert...but a full home install (as shown above) would be best left to the more expensive mason. They can cut/place the stone better than a tile setter. There are different techniques to the work which means bigger projects the domain of the master mason.

I think either wood that is the same , my first choice, or a tile look vinyl I really dislike tile floor in a space where you spend a lot of time in. Tile is hard on knees, feet backs and honestly are not water proof in a flood the wood underneath still gets wet and needs replacing.

How far does the hardwood extend on the rest of that floor. I would find out if you can find the same hardwood that is in the dining area, extend it into the kitchen and refinish the whole floor in a light color. Although I do like the darker floors. However, I would not rip out a good hardwood floor, just extend it and finish in a color throughout that you like.

You should be able to find a rug that works with both the floors and furniture once you've moved in. Don't worry until you have everything in your space. Look for a neutral to warm white for the walls - nothing gray. See if the owners can tell you what color is on the baseboards and doors currently. You could use that same color for the walls or one just slightly more saturated. You'll need to try the samples in your light, up against the floors. Wait on the cabinet color until after you've painted all the walls because right now the red will skew anything you look at. I can see a muted green or taupe on the cabinets with your granite.