LOOOVE what you've done. That's going to be stunning. I have a small pass through that I created where there was a door and went through this same argument with myself. In the end, I stayed with the flat counter and now that the top has been installed I can tell I'm going to love the extra deep space. My situation is quite different though. It's where I plan to do baking things, and while mine is next to the dining room it doesn't overlook it. It will also serve as a landing zone for things going in/out to the back patio. I'm assuming the DR will have a casual feel and get daily use. Are there views into here from other rooms of the house? I was going to say "flat counter" since it appears you want the two rooms to really function as one. But given that the sink is there I think I would go for the raised counter. You don't want to be splashing into the DR. Tough call.

Here is a link to google, how that backsplash should have been installed. There are some u tube videos too. I watched one video, where they used grout, between the countertop and the backsplash, and grout should not be used there. Caulking shud be done between backsplash and countertop. My backsplash is also caulked in all the corners, rather than grouted. Once you watch these videos and read these articles, you will see that your thinset was put on improperly, and thats why your tiles are falling off. Please read carefully. https://www.google.com/search?source=hp&ei=uI4VW7HdLszKjwTtrqSoAw&q=how+to+install+glass+subway+tile+backsplash&oq=How+to+install+glass+subway+tile+&gs_l=psy-ab.1.0.0l3j0i22i30k1l3.3755.12143.0.14244.41.29.3.9.9.0.173.3348.9j20.29.0....0...1c.1.64.psy-ab..0.41.3556...0i131k1j33i22i29i30k1.0.70wb9L5GlO8

lmao. what Jan said! Although, I had to help out my guys who did my herringbone wood floor. it's the starting point where everyone gets messed up. after that, it's simple. Look up how to properly start a herringbone layout and read it. you need to use a speed square at the end of your tile in order to get the proper middle starting point. much easier to illustrate than trying to write it out here. This is how I showed my guys how to start it. see the blue tape w/the two lines? you have to start on the middle after you mark your corner. that's the only way you will get perfect even cuts on both ends. this is how most do it, and it's not correct IF you want perfectly symmetrical left/right borders. All he's done is set the corner of the tile on the line. doing it like this will leave you w/one side smaller than the other: see how the sides of the window don't match? this is what you don't want. your tile guy should be doing a dry layout in order to determine where he starts so he doesn't get this look or these tiny triangles. Again,,,see how the ends don't match below? the right has longer tiles than the left edge. that's because of the way he started his first tile. And don't do these vertical tiles for your edging. get proper bullnose tiles, pencil liner or a Schluter edge. This is a layout board of my herringbone for my shower. took a few hours in order to get this almost perfect. since this was an odd size, and the tiles were even at 3x12, it couldn't be perfect. the right bottom corner triangle is the only portion that doesn't match. luckily, it's not readily visible! Even the subway tiles are perfectly matched. this layout took hours to get exact, even around the niche. 2x6your 3x9 will be 1/3 larger. 3x9 is a good size for a backsplash. this is a regular 3x6. again, a 3x9 will give you 1/3 longer.

Be careful where any light switches fall on that wall by the patio door. If they will be there you want them well within the tiled area and not half on and half off which ruins backsplash looks.