I agree with you the pillars are unfortunate. The replacement tiles will stand out no matter how close they come to matching so you're better off making sure they are clearly different so the gray one is better. Putting busy mosaic tiles could look nice but will interrupt the flow between rooms which I'm guessing is your problem with the columns in the first place. You will need to create a dextrous solution to tying into the 2x4 wall on the left side but I think it can be done tastefully- maybe beveling it back once you get past he end of that wall.

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.

I do not have any tiles in my current house but if you think about grout discolouring and looking bad.... then I think that might answer your question. My thought - the less grout the better.

I think, like you said, due to the fact that there's a larger space when it comes to the hotel lobbies is the reason as to why it works. I think that no matter what you put on the walls (whether it be concrete or marble) will result in tiles not working out. The industrial look tends to be exposed brickwork anyway, or cream or white colours so maybe that's an option you could look into. What did you end up doing?