Uneven walls are not flush with counter

When you install the tiles and grout at the meeting point between the counter and the backsplash you can cover the gap between them.

There are so many options, the best thing is to go online and get samples of the ones you like. Then it's easier to choose when you can put things side by side.

You can go to your local lumberyard and buy what is called 3/4 round wood trim. Cut to length and stain it or paint it and attach it to hide the opening.

I agree with Gk. I filled in a gap once, first with spray foam to fill the void (or things fell in), then add the molding (I used the one shaped like a "C"). Depending on your wall, there may be a neater way to fill it in. Depending on the tile, with mortar behind it, you will be able to fill some of that space in. An alternative method I used once, was after making sure the cabinet hadn't pulled away from the wall, and I built the wall out with wood until it was level without a gap. The gap you're dealing with sounds really large, so maybe adding sheetrock would bring it out better.

If I was doing it I would cut the tile piece so they covered that gap, so cut them to the space not the counter. Then when you caulk and seal it all will be hidden

Whoever put the counter on should have scribed the counter to the wall and either cut or grind it to fit depending what it is made of. Do not use any wood molding. It will deteriorate fast. Your best bet would be to find some trim or pencil tile that will fill/cover the gap. Always use caulk where backsplash meets counter. Just like around wall and tub.