It's probably impossible to match the white of the old and new tiles and if they aren't pretty close, it's going to look like a miss. It could be the lighting in the photos, but the floor tile looks more yellow than the wall tile. I would change it to gray, but I just don't like white floors either. 2+ years ago we moved into a house that has a bathroom with a white tile floor and it shows every fallen hair and speck of dust. The tile you like probably comes in gray. If you use gray you have sidestepped the whites matching issue. Just make sure the it is complementary with the color of the vanity as grays all have an undertone.

As for the wall color, the last thing you do is paint, so don't worry about that yet. Test a large swatch before doing the whole room. Sea Salt is a very popular color in bathrooms and I don't think it looks like it only belongs in a child's bedroom, so go ahead and try it. The issue there is going to be partly whether it matches or clashes with the vanity, and also like you say, if it's just too much blue-green in the room. If it doesn't work out, look at off whites with an undertone similar to the color of the vanity.

I was kind of thinking the same think about the two white tiles not being the same shade of white. Also, I insisted on white grout a black/white bathroom floor and I regretted it--really hard to keep clean. I'm not crazy about painting the walls a close color to the vanity. Perhaps a colored tile on the floor and keep the walls neutral. Good luck with your project!