sorry, but that was very poorly done.

you don't need a side splash (there are other options) , certainly not one done in that manner.

This one is also incorrect. they're too thick. they probably cut the backsplash piece from a leftover piece of the granite.

But, at least it's sitting on top.

This is your basic Lowes, 30" vanity and countertop with a 1/2" overhang. looks like a 2-3" backsplash piece, installed correctly. they have a budget/basic 4" spread faucet.

This is an option. (wall treatment like this shiplap on the side) or you could use tile.

But if you feel you really want one, install the vanity/countertop, and the side portion goes on top. It should NOT be done like your current one.

here's a pic of one we did on a budget redo but someone

Sits right on top, along w/the piece across the back. (BTW, if you do a wall mount faucet, you'll gain a lot more countertop space and easier to clean)

this lined up fine w/the plumbing

you're getting a new vanity w/a diff countertop? any idea what type?

The measurement of the vanity is usually 29-30" (for that size) with a 1/2" or so for the countertop overhang. You shouldn't have to worry about moving your plumbing.

The rough-in should be able to serve a slight shift, but the drain will be replumbed.

The plumbing change is slight and not an issue.