Melt it with Goof Off.
yes
You can glue the tile down, only concern is there enough room for the door to clear the tile?
Use petrol or paint tinner...
Yes, if the adhesive is smooth, no lumps and if you use a compatible glue, not thinset cement
Yes, you can (but there are many cheaper ways of doing it , such as regular tile glue)
Scrape off carefully with a very sharp craft knife with blade held almost parallel to the floor.
You can put the newer style floating wood floors onto a floor with tile. Also, if it is old VCT tile, there are glues that will allow you to use their product to glue the wood to the floor. Unfortunately, nail down wood is not acceptable.
The glue used to stick them to the floor is weak, or there was dirt or foreign matter under the tile, or the under floor was not completely clean when it was laid.
You're mum got laid last night.
A vinyl tile glue will do that -Mapei Ecobond, in Home Depot.
Not directly as the ceramic tiles will soon show through the vinyl flooring. If the ceramics are laid on a wooden floor, you must take up the tiles and overboard with 6mm plywood. If the tiles are on a concrete floor, you can leave them down and lay a latex screed on top to provide you with a smooth floor for your vinyl
If it has a timber floor under and vinyl is solid to the floor and not to thick screw down 10 mm ply at 150mm centres. seal ply with pva sealer prior too tilling. If it is a concrete floor it is best to lift vinyl.