The overflow can be lifted so that the fill valve can be adjust to allow more water into the cistern.
But it is probably blocked with limescale, put on some rubber gloves and clear the holes where the water flows into the bowl, with a small screwdriver.
Andy
Lay the shower head on the base of the shower tray and turn on the water so that it is flowing into the waste, do this for 10 mins and check if it is leaking below. If not then the leak is due to the shower door, silicone or tiling.
If the waste is leaking then you could cut a hole in the...