Tile is still the best thing for a walk-in shower to be waterproof. Neither the cork or hardwood will be. Think about installing a radiant floor under the tile like Sharon recommended. I like the NuHeat Radiant floor system the best.

Get the professional sander guys in to repair the living areas and kitchen but don't go too dark with the stain as it will kill the lovely grain in the matai. I'm thinking a couple of tones richer than the timber knots showing in your photo, definitely no yellow tone at all. In NZ stepping on to carpet especially in a kiwi winter is so much nicer than a cold floor board shock!!! A nice area rug for the lounge and you're done.

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.

Flooring should be light. I'm not sure how a bamboo floor would work. Did you end up going ahead with the kitchen plans? What did you go with?