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..

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.

those tiles from the 1800s are encaustic... the color goes all the way through. ceramic tiles are red in the middle and have just a relatively thin layer of color and glaze. porcelain tiles do have a color matched center (look at the edges to tell) but i'm not certain that all of the pattern goes through. at least it would wear off and turn the main color, not red.

after watching my daughter and her husband agonize over the way their expensive timber floor has not held up well after 3 years, I would recommend tiles/wood look tiles with under heating. Their beautiful warm expensive floor looks like it always needs a clean and polish, not from neglect, they have cared for it well. One of the boards now has a slight and painful moan when it's stepped on :-( I grew up in a completely wood floor home and although it looked wonderful, my Mother hated it. ....and the mats ! Wood is a lot harder to maintain than tiles ,(no matter what the die hards say) the modern wood finishes are much better than they used to be.... But a piece of wood is rather arty no matter what it's used for and it does demand to be loved and cared for.....and if something goes wrong it's a lot more expensive to fix than sand and cement. Ultimately you have to be happy. BTW underheating tiles is warmer than timber :-)