That's all a matter of preference. Not seeing the tile, I generally prefer diagonal. For some reason I prefer not to have all the lines in the same direction, so having the tile at an angle to the wall and cabinets just looks better to me. But some people don't like that at all. There's some good discussion on this in Bathrooms if you want to do a search and read while waiting. No feelings about grout lines other than I know I can't keep them clean, so I would go small. Not sure if these are regular tiles or vinyl, but for regular tiles make sure you ask about lippage. That's when the tiles are not even heights, less/no lippage is better, but harder to do. I don't know all the technical stuff, but good info on Bathrooms about this too. Maybe just bringing it up will encourage them to be on their toes?

My first thought was slate too and there are ALL kinds that would look great in that situation and hide dirt at the same time. We have what's called Indian Autumn in our master bath which hides dirt super well. And then there is Quartzite stone (not to be mistaken for the counter tops) that is harder and less porous than slate and hides dirt as well. We have this as our backsplash in the kitchen. I think this would be beautiful with the brick you described.

I'm barely getting the idea of the exact cabinet color, and I'm not too familiar with the 2 walnut finishes you're considering, but I can advise you to get the one that is the most 'forgiving'...If it lets some light coloring and grain show through, you will go less crazy keeping up with dust and any pet hair. We have Brazilian Cherry floors and they rarely look clean. I thought they'd be a 'medium' choice and that the cleaning wouldn't be that big a deal, but it is. The darker the floors, the more scratches and dust show. With busy, growing kids who are home all day, I wish we could spend less time on the floors, and that they'd look better more of the time. I also had to write, because I also have been blessed to spend my days with my kids and started homeschooling my daughter when she was in 1st grade...and my son was 5, and my younger daughter was almost 2! Sound familiar? ;-) We added 5 more to our family after that, so I'm still homeschooling and those oldest 3 are now 20, 19, and 16. My oldest daughter is in her jr year of college. Time flies! I hope your kitchen is planned with plenty of room to enjoy hours of enjoyment cooking and baking with your helpers. :-D

It happens all the time. A homeowner will choose a tile or type of flooring and the installer will install it without thinking. Tile and flooring is not something that you can just throw down and make it work and come out even especially on a remodel. Here's why.. You start out with all of the subfloor heights even. You decide to install 1/2" thick wood flooring in all of the rooms but the kitchen. When new the builder compensated for the extra height when they tiled the kitchen. Say for example 1/4" thick tile was used. The builder would add 1/4" thick plywood to raise the floor to where the tile would be even with the wood flooring.. Fast forward.. You come along and decide to redo the kitchen floor with 1/2" tile that calls for a 1/4" underlayment. You now have 3/4" total height to deal with. The old 1/4" tile is removed. Minus 1/4 from 3/4 you have 1/2 left. !/2" will be the difference in height between the old and new. So now you have three choices. Go back and find a tile or flooring type with a thickness that will come out even when fully installed. Rip out all of the old wood flooring throughout the house and start over. Add a transition piece and learn to live with it. Myself I would have did a lot of measuring and after if you wanted to go with the tile you choose. Then I would have added something like a Shur-Trim transition piece under the tile and onto the wood flooring.