Home Improvement Questions? Ask a Handyman for Answers
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You can't tile directly on a plaster wall. You either have to remove the plaster and install backer board or you could use 1/4" backer over the plaster but that would leave a 1/4" gap at the top of the tile where it stops on the wall which you could hide with a tile or wood molding. You must remove the vanity and the toilet before you tile the floor. Walls are usually tiled first so as not to damage a newly tiled floor.
How thick is the sub floor? Yes, vanity and toilet go on top of the tile. You'll probably need to build up the height of the toilet flange so it's above the top of the tile. You can use a flange extender kit for this purpose (see attached pic).
I suspect your subfloor is more than just 1/2" plywood at least it should be. The subfloor is the flooring beneath the underlayment (from the top of the floor joists)or in this case backer board. So if the top layer is 1/2" there's usually another layer of 5/8" ply beneath it. If there isn't then tile industry standards call for at least 1 1/8" of wood beneath the tile.
That will work. I'd appreciate a favorable rating