Most ceramic tiles are laid over a wooden subfloor, except for those on the ground floor of a house with a slab foundation.
I will add to the answer above by saying that you will need to use a polymer-modified thinset morter when installing ceramic tiles over wood. Most tile-setting morters available today are "modified", but check to be sure, because regular morters are designed to be used over concrete and will not adhere properly to wood.
Also, if the floor area is large and there is more than a tiny bit of flex in the floor, you might end up with cracked tiles, especially if you or your family or guests are heavy. To avoid this, it might be necessary to build up the thickness of the floor by adding another layer of 3/4" plywood, or by using the older method of wire mesh and concrete over the existing wood (in which case you would not need a modified morter).
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I would get advice from a professional. I suspect that the cement backed board (plaster board?) would crack and turn to powder under the flexing as people walk across the floor.
Yes, but I wouldn't recommend it. You will regret it later. Tile needs a cement base to adhere to. A wooden base is not good for ceramic tiles. I have seen tile floors where people have tiled over the wood. The tiles are loose, cracked and unlevel. The grout is coming out and water seeps through the floor.
Tiles used on floors tend to be thicker than wall tiles. Also, floor tiles are subjected to flexing as people walk over them. Therefore, if floor tiling a wooden floor, use a flexible cement adhesive and grout designed to give and take without cracking.
I have tiled over cork tiles with ceramic tiles and it worked fine in a bathroom, around a bath. If the current tiles are really well fixed it should be fine.
It is possible but I would not reccomend it. If possible remove the old tile before laying the new tile. If you want to avoid removing the old tile you can lay a cement board over the old tile before installing the new tile.