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.

Absolutely no problem changing up the carpet. Things to watch for......make the transition in a doorway, an opening or along a visual break in the rooms (like the corners of the walls). I would stay in the same colour range, but just go to the other end of the spectrum rather than change the colour completely.....like light grey going to dark grey, not light grey going to navy blue. You want the separation but an easy transition on the eyes.

Love blue tiles. Depending on how much sun and how hot your pool gets in the summer should dictate what color it is. We live in Arizona, so cool blues work best. Our neighbor has brown tile and a dark pebble tech pool. Looks like a swimming hole and gets really hot - 94% water in the summer. They obviously didn't think it through.

Paint your house and ceiling first. You are probably asking for trouble if you put the floors down only to paint over the top of them. If you can, remove the tiles in the kitchen and paint just behind the line of the splashback too. Once painting is done replace kitchen benchtop then splashback. I would call the bathroom its own job and do it individually, unless you only need to paint the ceiling and if a tiler doesn't need to be brought in for anything else in the house? A lot of bathrooms now are getting tiled from floor to the ceiling if this is the case, paint the ceiling first, then tile. If walls need to be painted, it wouldn't really matter if you did them first or last, though if you did it first expect to do some touch-ups. I guess if you really wanted, you could do the first coat before tiles then second after... I don't exactly like stopping and starting painting, so I would do the walls (if they needed to be done) in one hit, after its been tiled. Well that's the order in which I would do everything... Really, for what you're asking, the painting could be done at anytime, but to make life easy on yourself, I would definitely recommend doing it before the floor.