Yes you can if you first rough up the ceramic by sanding it. Use a vinyl mastic like Mapei Unibond.
A vinyl tile glue will do that -Mapei Ecobond, in Home Depot.
It depends on the type of ceramic adhesive. Many of them can be taken off tile with lacquer thinner on a rag.
Epoxy or silicone.
if it is glazed ceramic tile - let it dry fully (I let mine dry for a few weeks) then CAREFULLY pop the glue off with a chisel. Hold the chisel so the flat end is up and the beveled end is on the tile and gently push the tip of the chisel into the (expanded) gorilla glue. hit the end of the chisel with the palm of your hand and the glue will pop off the ceramic.
yes
Any epoxy or LePage Extreme or PL200 would work for that.
Yes, soften it with Goof Off, then scrape it with a craft knife, blade almost parallel with tile.
Yes, if the adhesive is smooth, no lumps and if you use a compatible glue, not thinset cement
If the carpet glue is dense enough to affect your tile cement then you should remove it by sanding. -If it's only sparse then it won't matter.
Yes, you can (but there are many cheaper ways of doing it , such as regular tile glue)
You're mum got laid last night.
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