Could there be an all-water planet?

The outer planets have several moons that are made primarily of water ice, including some of the largest ones in the solar system. If they were closer to the sun, they might be totally covered in oceans hundreds of miles deep. But they have rocky cores with little or no iron. If unable to sustain an atmosphere, all that water might evaporate and be carried away by the solar wind.

Yes theoretically, as you went deeper in to the planet the water pressure would increase and at some depth the water would become solid, deeper if the planet is big enough the solid ice would be under sufficient pressure that it would begin to take on properties of metal. I would expect that any planet would have a rocky or metallic core down deep made of silicate rocks, iron and nickle.

All water no - you need a nucleus to act as an attractor, water would sublimate to space in the early low gravity stage.

But given a rocky core and fair distance from a star (lower temperature lower energy for those water molecules) you could get up to a 1G planet with no exposed land and a very very deep ocean.

I don’t think it would be possible. I mean, there can be a planet where there is water over all the surface drowning down all possible land, but maybe not one where there is 100% all water.

Some moons in our solar system are all water.