What can I do about water leaking behind the shower tray?
Tile over green drywall is not waterproof; you will get water migrating through the group and into the drywall. The best thing to do is to tear down tiled walls, put up a new solid backing, and then put a waterproof membrane over the backing. Then tile goes on the backing.

Kerdi is a common backing, and that will be waterproof on top of a drywall backing, though I'd probably use a fiberglass-reinforced version.