This kind of tile on the wall is one of the most annoying to remove. There is the tile, then about an 1"-1.5" of concrete that is held up and together by a very sharp metal mesh. It's very strong and to take a hammer to bash up the tile tends to also damage the plaster/drywall in the adjacent rooms. You need a 7" angle grinder along with hammers, and pry bars to remove the tile successfully. I have done this many times and recommend if removing the wall tile you take the plaster/drywall on the walls above the tile off too. Just re-drywall all of the bathroom walls, because seaming the old plaster with then new drywall isn't easy or worth the time. Tends to be different thicknesses everywhere and you'll need furring strips... not worth it.
You can re paint the tile with the kits they sell at home depot. This will temporarily make it look better but probably only last 2 years max before scratches and chips show the blue and pink. I recommend just taking the walls out. In the long run I think you would be happy you did.
As for the floor you can lay ceramic tile on top of the existing ceramic tile. Yes it will raise the floor higher than the floor outside of the bathroom, but only about 7/8". You can buy thresholds for this to make it look ok.
If you did decide to leave the walls and lay ceramic tile on the floor, get the tile as close as possible to the wall and use grout caulk that matches the grout to fill the seam.
I have also seen People liquid nail wainscot to the wall tile and put a brick mold on top as a chair rail to cover the gap. The only issue with is the wall tile probably goes into the shower. You would then have to reglaze or repaint the shower tile and tub.
Hope this helps