Flooring Tile - Bath backsplash

Going to buy tile etc., for master bath remodel.
Want to add a tile backsplash above the sink and vanity. The countertop already has a 3 inch incorporated backsplash as part of the design. Will be adding 6 inches of tile above this.
It's a 5' long countertop with a sink on one end, makeup area on other end.

Do I need to remove drywall and replace with wonderboard? I know that I probably should to be safe. But it's in fine condition and would only see the occasional splash of water. If I left it as is, will I be kicking myself later?

And as a design feature, should I continue this backsplash on short side in corner? Counter sits in corner, so tile both long wall and short?

This is not really a wet area, although it will see some splashes here and there no doubt. If the drywall has not yet been painted you are all set to go. You can use a modified thinset for this. If its painted but in good shape, rough it up with sandpaper, clean off the residue and use a good modified thinset. You dont need cement board here.

Tiling just the back, or the back and the side is really a personal preference. I think it would look best if you did both. Caulk the joint between the tile backsplash and the vanity top.

I have read this with interest and I am getting to be putting some tile in the bathroom above a tubsurround. Like the sink job that is being talked about it does not get direct contact with water. It is drywall covered with wallpaper right now. I was planning on taking the wallpaper down and just putting a white 4in tile instead of the wallpaper. So what is the modified thinset? Will it be labeled as such on the bag? Thanks.

Modified thinset is a thinset that has a latex or polymer additive in powder form mixed in with the cement. The additive allows the cement to bond to non cement substrates like wood or wallboard. A modified thinset will say so on the bag, usually costs about $15 and up, depending on the amount of additive put in the bag.

Johnny...
"Caulk the joint between the tile backsplash and the vanity top."

I should keep any of my tile from touching each other or other surfaces, right? IE...where wall meets floor, should have a small gap filled with caulk...same at ceiling, inside wall corners and where tile meets sink?
I assume the same goes for avoiding thinset in those gaps?

Yes NCR you have it right. Caulk all changes of plane.