Yes very possible, are you planning to replace it with something or just leave drywall?

Think of the layers, you have the chalky like core of drywall, the paper covering over the drywall, possibly paint over the drywall, the mastic or mortar holding the tile and the tile. You will pry up the tile with something like a 1" putty knife and something has to give for it to come off. It is most likely to be the paper on covering on the drywall although you will probably find a few spots where you have poor adhesion to the mastic so a some tiles will let go whole at the mastic. Then you have mastic or mortar that needs to be removed from the wall if you intend to paint. Usually not an issue if you are going to tile back over it.

Bit of a messy project but very doable.

With the right tool you can do almost anything. You want to use the Fein Multimaster with tile kit. There are tons of videos on this on youtube, as in the link below.

I will tell you that removing glass tile sent me to a hand surgeon a few months later. I had cut myself on a tile and then realized I had a glass shard in my finger that had to be removed. Including X-rays my DIY experience cost me about the same as it would have to have a pro remove/re-install the tile, so be careful, wear heavy gloves (not thin nitrile ones) and eye protection, and get a couple of quotes first.

Here is a link that might be useful: Fein

Yes.

FIRST you need to slice through the grout lines between the accent row and the tile you want to preserve.

You can use a "grout saw" or any number of small power tools, like a "multi-tool" with the right kind of blade.

Run a line of masking tape along the top edge of the tile you want to preserve, then slice through the grout.

Then slice through the grout lines between the accent tile rowss. You want to limit the amount of tile that will get pulled or pried off.

THEN: Cover the counter with cardboard to protect it from flying tile bits. Also wear eye protection ... shards will fly sometimes.

Then make a few vertical slices through the grout in the accent tile rows and gently pry it off the wall. If you tap a thin spatula or paint scraper between the tile and the wall you can often pop the tiles off with little damage to thew wall. Keep the blade of this tool almost parallel to the wall and tap with a small hammer.

lazygardens, as just a curious bystander, I want to say what a clear, illustrative description you just gave. I can picture it perfectly! Good luck, cindee!!

I would plan on replacing the sheet rock behind what you remove. Unless the tiles were poorly set chances are you will (at minimum) tear paper and more likely completely rip some off. Not much stick well to the core of sheet rock and it is a bear to fix so it works. Lets say that I have not yet seen a backsplash removed that did not fatally damage the rock and don't know a tile person who would put new tile onto damaged rock.
Replacing the rock is no big deal, hardest part will be cutting pieces that narrow- you might also want to put some durabond in the seams. That must be done carefully and neatly so there is no excess as it does not sand well, but it does stick to raw sheet rock.