Render + waterproofing for existing shower wall (brick wall)

Hi mate. Technically it's impossible to repair the waterproof membrane correctly in this situation as the WPM is meant to be continuous and obviously will now have breaks where they join.

All you can do is patch the float out to the correct level in the areas where it's been removed. Try and keep all the junctions as clean as possible. Then I'd mask around the remaining tiles and run a ring of masking tape around the mixer body at a depth that will be covered by the tile and cover ring. Then run a small bead of silicon around the mixer body and wall and smooth it off to act as a bond breaker. Then waterproof all the new float and onto the mixer body, covering the bead of silicone. If you can get some waterproofing onto the edge of the existing tiles but where it will still be covered by grout, then that's about as good as you can do. When it's tiled don't grout around the tap leave it clear and silicone it.
If I was doing this for you I'd get you to sign a waiver on the waterproofing as the only way to do it correctly is to remove all the tiles and redo the waterproofing as a continuous sheet all the way back down to the drain.
Most houses in WA have inadequate waterproofing anyways so to be honest you will probably be ok if you follow what I said.