first, Briwax won't do what you want. I'm a pro wood finisher with cabinets and wood furniture. If your cabinets already have a clear coat on them, (and the should) the wax is just going to sit on top and get waxy and yucky w/attracting grease and grime. that's a hard NO on using wax on kitchen cabinets.
You've also got red oak. red oak already naturally has a pink tone. The pickling stain has muted it, but not enough. short of stripping them, staining, or painting, you're not going to change that look. Work with it, not against it.
I suggest you look at tiles and countertops that work w/the pinkish/white tones, and forget about any blue grays or overall 'grays' for now. Some gray is ok, if you can find the right shade to work w/that wood. you'll have to get a lot of samples.
Forget the backsplash for now. It's useless to try to even consider anything without getting your lighting, flooring and countertops.
secondly, you can remove that florescent fixture yourself if you can DIY, and replace w/something like these
You'll be left with what's in Pic 3. patch and repair around the ceiling, and install the guts to whatever light fixture you decide on. If going w/recessed lights in all of the kitchen, the electrician you hire will do all of this.
The key to good lighting w/one of these is multiple bulbs and using a 4000K bulb. nothing lower or it will cast yellow.
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Lighting info
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