Scrape off as much as you can with a putty knife or paint scraper, then use an adhesive remover, such as Peel Away or Goof Off, available at home centers. Do NOT sandblast. Here is a link that might be useful: Peel Away

Nothing is going to work for long if you don't fix the problem of shifting. The cracks will keep getting bigger and anything you put in them will fail.

I use the Mr. Mister mop with BONA and microfiber cloths from Solutions. I have wood floors in every room except the bath and laundry. The mop is handy because I can put the BONA inside, but the head tends to flop around and you have to refold/change the cloth every so often. I find it easier to just get on my hands and knees unless I'm doing more than a couple of rooms at a time. I have never used it dry. I don't baby my floors, but those Solutions cloths are very *grabby*. I'd be afraid little rocks would get caught in the cloth and add more scratches to the floor. Before mopping, I use a regular old-fashioned dust mop to push everything out the front or back door. No kiddies here so I don't have to mop very often. I sweep or vacuum every few days and spot clean as necessary. I believe BONA is short for BONAKEMI. I purchase the big jug of floor cleaner from the Bona website. I also use it to clean wood furniture and cabinets - I haven't bought Pledge or Murphy or Endust or anything like that in ages. I could be paying way too much for the BONA. I've never comparison shopped it.

Unfortunately dogs do occasionally splatter things on the wall. Sometimes it's slobber or ear gunk. I just fill a bucket with water and some dish soap and scrub it off. I usually only use magic erasers when it's dog toy skid marks on the wall.