No plate below. It will drip on to whatever is below it.
3/32 should work
I think it's stainless with brushed nickel finish....shouldn't rust
Figure out where you want it on the wall (it helps if there is blocking or some framing behind the tile in the area you want the soap dish placed. If not you'll have to use the wall anchors.. Place the mounting base in that location and mark the two holes. Drill the appropriate size holes using a diamond tile bit using a spray bottle to keep the drill cool.Go slowly this is not the time to rush. Before you screw the mounting base to the wall apply a small dab of silicone sealer to the area where the holes are. This will help to keep water from entering the holes you just drilled. Fasten the base to the wall and the soap dish to the base.