If you are talking about ceramic or porcelain tiles then yes. Granite tile and counters can also be cleaned using acetone. For softer stones like marble and travertine I would recommend using petrochemicals.
You sweep the floors
Acetone or lacquer thinner should do it.
"Goof Off grafiti remover" or Acetone
finger nail polish remover, or acetone.
It depends on the type of ceramic adhesive. Many of them can be taken off tile with lacquer thinner on a rag.
Probably acetone (nail polish remover).
Get a tile cutter and remove the tile. Strip all the tile off and make sure the underneath surface is clean. Then u install a protective foam pad layer and install the carpet above it.
If it's silicone, as is likely, then get most of it off with a sharp edge of a craft knife and the rest with acetone or lacquer thinner on a rough rag.
You CAN place tile over tile, but saying you can put tile over tile is like saying you CAN jump off of a bridge. It's just simply not a good idea. It can cause air pockets to be created under the tile laid on top, which can lead to cracked tiles if anything is dropped on them or sometimes simply by walking on them. It's worth the time to go ahead and strip the tile off of the floor before laying any new tile.
Nothing wrong with windex, it will work ok & not harm Porcelain but may not get everything off it.
To clean perfume off tile floors, mix warm water with mild dish soap. Use a soft sponge or cloth to gently scrub the affected area. Rinse the floor with clean water and dry it thoroughly to prevent any damage to the tile.
Plywood is the best choice between these two. Particle board can swell if water gets to it. You would be better off if you use a tile backer board. Concrete based or a fiber type. They are made for this application.