Mineral spirits is also great for the general grunge that is made up of dirt/dust mixed with skin oils, like you get on wood banisters, wood chair arms, etc. I've had much success with it: my folks learned this in a furniture refinishing class. If the furniture is just deeply dusty without grunge, though, it may not be necessary. I've brought furniture from the parental attic that was just deeply dusty in the carvings. For that I used a vaccuum cleaner attachment in the left hand and a clean white china bristle brush (stiff bristles) in the right, to dig out the dust while the vaccum nozzle followed behind. The vacuum attachment with bristles was too soft to be much good.

If you want to waterproof the tile installation, one of the common ways is to install a material like Ditra, and use that as a transitional material going from the subfloor to the tile. Ditra comes in rolls, if the installation requires more than one width of Ditra, the seams are not waterproof. The seams can be covered with a strip of Kerdi or Kerdi band. A strip of Kerdi band can also be used at the floor perimeter, especially behind the machine. Have the strip of Kerdi run from the Ditra at the perimeter of the floor and turn it up the wall a few inches. It'll prevent water from escaping the room under and behind the baseboard. You don't have to technically turn the laundry area into a wet room. You're just looking to minimize damage. There are other membranes that can be used under the tile as well. I do recommend using a pan under the washer if it's a top loader because of the sheer volume of water that a top loader can hold. I recommend it for front loaders as well, although they do hold much less water. A typical pan is about 30"x 32" x 1-1/2", that's large enough to contain about 6-1/4 gallons of water. Since you have a floor drain, that'll help prevent pan overflow. For the most part, that's good enough for a basic leak with the washer itself. Now, if the machine is leaking on one end and water is still being supplied to the machine from the other end? A flow-through type of leak can possibly overwhelm any drain set-up. I highly recommend an automatic water shutoff system. I installed one in my own second floor laundry. I have a pan with a floor drain as well. There's a shutoff valve for each water supply. I have a couple of moisture sensors, one under the machine in the pan, the other outside of the pan, against the back wall. If either sensor detects moisture, the hot and cold supply valves will automatically close and an alarm will sound. It has a battery backup. Pitching the tiled floor under the washer? It sounds like a nice touch, and it does provide redundancy, but I don't see it as necessary. Provisions would also have to be made so the washing machine can remain level.

My home is small so I moved all my furniture as far from the work as possible. That way no one could bump into it. I bought some 9 x 12 ft vinyl drop cloths for less than $7 each with tax that are supposed to stay put better than plain plastic, but I have nothing to compare them with. Another thing that can be done is to tape plastic in front of openings to other rooms to keep dust out. Remember that a central heat/AC system could pull dust through it to the rest of the house. If you can't isolate the kitchen while the work is being done it's best to use a better or best quality filter and change it weekly so as to catch ultra fine dust. Hope that helps.

I think the contractor who had the bathroom problems was probably exactly like that at home, I don't think it was intentional at all. I worked in an office building with a bathroom in the central core rather than the office suites and the floor was populated by Drs.-, Lawyers-, and Financial Services offices, and the things that would happen to those Key-Accessed-Employee-Only restrooms was absolutely Incredible. I left I note in there once that someone who regularly used that bathroom needed to seek psychiatric help. Anyway. My dad took a Second part-time job in a different hospital which lasted for a number of years to pay for the interior design and furnishings of their new house. We were allowed to use the entire house, but we weren't supposed to eat, or use things like markers in the living room. My nieces and nephews called the LR sofa the napping sofa, because it was a quiet place to go read a book. I have it now.