If you have good ventilation and no small children who might decide to decorate with crayon, beadboard should be fine. We (our contractor, actually) put in beadboard when we redid our front bathroom four years ago and there has been no problem whatsoever with it.The BR originally had black and white tile that was cracked, chipped, and stained, an awful mess. When the tile came off, so did whatever was behind it, so those parts of the walls were down to the studs. I don't recall what our GC used behind the beadboard, but it is very solid and there hasn't been a trace of mold. We painted it a white that matched the Daltile that went up on the tub surround. To clean it, I use one of those mild kitchen and BR sprays - like Windex - and a slightly damp sponge every so often, but really, upkeep is no problem. For ventilation we have a jalousie window over the sink (original to the house, from 1933, not code today, but we love that window). I leave the window slightly ajar most days and that's all the ventilation we need. I think white beadboard would look lovely with your floral wallpaper, very cottage-y, one of my favorite looks. You could pick up the colors of the wallpaper in your towels and an accessory or two.

It all depends on what they used to install the tile and the condition of the concrete. Best case scenario was very smooth/shiney concrete with a non-modified thinset mortal, which the tiles pop easy and the thinset can be scraped with a standard flooring scraper. Worse case scenatio was rough concrete installed witha modified mortar. Tiles come up in little pieces and the thinset is now a part of the concrete where you take off the high spots and feather it out with floor patch or you need to grind it. There is middle ground if the concrete was shiney and smooth and they used modified mortar. Do a test with a hammer and cold chisel to see how easy it will come up and scrape. If its very tough, go rent a small demolition hammer with a 3" scaling bit.

Protect your wall tiles with cardboard and take a hammer to the row of counter top tiles that are against the wall. Break them up good. Wearing gloves and using putty knives and screwdrives pull out all the little pieces of tile from that row closest to the wall. Wiggle them out from under the backsplash tile, they should come out fairly easily. This clears a distance the thickness of the tile for the counter to pivot up upon removal before it contacts and loads your backsplash tiles. If that proves to not be enough set the depth right on a circular saw or rotozip and zip through the cement board and pry that off too. It will take more finesse then normally is used when demoing kitchens but with a little caution, it should be very doable.

Yeah. That’s gotta go. Hmm. I would pull the range out, cover the adjacent countertop with plastic, cover the floor with a fat, folded canvas drop cloth, put some acetone in a spray bottle, saturate behind the top edge and let it run back in there, then go at it with gloves and a Cable saw. Rinse, repeat. Acetone may not help — but if there is any adhesive back behind it, it might soften it a little. If your floors are hardwood, put a plastic drop-cloth under the fabric one first. It is a crazy long shot, but might work a bit better than a hammer. Worse case scenario, you can go back with a stainless backsplash panel to hide any damage to the original tile.