I am far from an expert, but here are a few ideas I had: 1. Turn the S. Toilet into a laundry room. Maybe pull the wall and door a little to the right so it lines up with the shaft wall above. If you can, use a pocket door that drops into the wall below so the door does not swing into the laundry room. The wall at the top where the door swings into now could have a fold-up or down table 16-20" deep when open, that would lay flat against the wall when not in use. (The table would block the door way when in use, but would give the person inside the room a place to fold clothes, or you could fold them at the kitchen table.) Depending on how you place the items, which depends in large part on the window, the room should have space for a washer (plus stacked dryer if desired), utility sink, a small amount of cabinetry or shelves to hold laundry supplies, and maybe a bar for hanging clothes. 2. Turn the utility room into a walk-in pantry. Put shallower shelves (10-14" deep) on the left side and deeper storage (18-24") on the right side, leaving at least 3 feet in between. The right side could have a counter top area with cabinets below and shelves above. The counter could give you a place to store and use any small appliances you do not want out in the main kitchen (microwave, crock pot, toaster oven, etc.) If you want a larger laundry room, leave the laundry in the utility room and put a smaller walk-in pantry in the S. toilet. 3. Get rid of the walls that create S. Room so that the kitchen is now an L wrapping around pantry. Use a small round table and 4 chairs for casual in-kitchen eating. 4. Either buy a counter-depth fridge or use deeper counter on left side of kitchen with standard depth fridge. With a 9' 10" wide space, you could have a 30" deep counter on the left side, a standard depth counter on the right side, and still have over 5' in between, which is wide enough for a 24" dishwasher and sink base of up to 36" at the top end. 5. There is a lot of wasted space next to your powder room. Assuming you could use more storage space, I would move the powder room door to opposite the sink. Then you could put a reach-in closet on either the wall next to the powder room (as shown below) or against the wall between kitchen & dining/foyer. If you want even more storage, a small walk-in closet could be placed next to powder room. Please excuse poor drawing - this is the first time I have tried to do this.

Here's a look at how I did it for my bbq and firepit. We used stone for all vertical surfaces, and repeated the travertine pavers for the horizontal surfaces. However I do wish that I had used granite for the countertops instead. My house is stucco as well. I think stucco rather than stone on everything but the columns would be fine too (and cheaper), but stone on the columns really adds a nice touch. My columns were originally stucco but I had it replaced with stone. I don't have a handy photo of the columns and patio, but I can snap one if you'd like to see them. Here's the bbq. Don't forget about lighting!

While we understand you only asked for back splash advice we also look at the rest of what you show us and as pros are inclined to point some things out. Sophie is right when it comes to the range area. We usually leave a minimum of 9" in width between the stove and the hood columns. Fire harzard issues not to mention grease and damage to the cabinets. Base on the picture you provided it shows there is barely any space between the hood columns and the stove top. For back splash we will need a picture of the door finishes in the main kitchen. Counter selection and floor selection.

I dont know what is that tip, I didn't write that, sorry. So, to much the exact color with the rest of the cabinets, when we design the kitchen islad, we look everywhere for a manufacturer stickers, the previos owners mast removed them, and we had a very difficult time finding the color but we got preaty close. Now that u mention, it may not be wood at all, some stain plywood or similar that I may be able to work with. And if is plywood, and stain, I can only sandpaper it !...or I can cover it up with primer and paint ?