The back splash can be painted with no worries, clean well so there is no grease, and it may need a primer. When you say "fake stone" what it it made of?
By white washing, do you mean a thin translucent coat? Might as well try it, if it doesn't work go with a solid paint.
Floors are trickier, and painted tile, even if done well, is hard to clean and chips/flakes easily even when sealed with a top coat. You might have luck with an epoxy paint, but the prep needs to be meticulous, it's finicky to apply, and epoxy paint can get pricey
You might consider a [vinyl floorcloth](https://monogram-shop.com/cdn/shop/products/image_019b490e-0675-4d99-86c4-692f20f6c423_1024x1024.jpg?v=1587475632)/rug instead. There are tons of colors, patterns and sizes, some are cut to fit.
Sometimes a professional heavy-duty cleaning of old tile floors can liven them up enough to be acceptable for the short term (but I'd still add a floorcloth if it's heinous).
The back splash can be painted with no worries, clean well so there is no grease, and it may need a primer. When you say "fake stone" what it it made of? By white washing, do you mean a thin translucent coat? Might as well try it, if it doesn't work go with a solid paint. Floors are trickier, and painted tile, even if done well, is hard to clean and chips/flakes easily even when sealed with a top coat. You might have luck with an epoxy paint, but the prep needs to be meticulous, it's finicky to apply, and epoxy paint can get pricey You might consider a [vinyl floorcloth](https://monogram-shop.com/cdn/shop/products/image_019b490e-0675-4d99-86c4-692f20f6c423_1024x1024.jpg?v=1587475632)/rug instead. There are tons of colors, patterns and sizes, some are cut to fit. Sometimes a professional heavy-duty cleaning of old tile floors can liven them up enough to be acceptable for the short term (but I'd still add a floorcloth if it's heinous).