you can either put up more plasterboard inside the shower screen and pack it out or chisel into the plasterboard and wood to let the tray sink into the wall
Can't really tell,if it's wallpaper you should be able to peel it off,if it's artex which I have never seen it on a wall you can take it off sealing off the room, using protection and a hoover
I had exactly the same,it looks as the wood is decaying only on the top so needs sanding down,then paint it with oil based fencing paint and then cover it with upvc fascia board
You have to carry on feeling the pipe upwards as water runs down and the leak could be further up the pipe,my guess is that it's coming from the connector that joins onto the sink tap