Are the continents floating on water?

Continents are not floating on water. While it is true that the Earth's crust is divided into tectonic plates that move on a layer of molten rock called the asthenosphere, these plates are not floating on water. The plates themselves are made up of solid rock, not water.

Additionally, the plates don't "float" in the traditional sense as they are not buoyant relative to water. Instead, they move due to convection currents in the asthenosphere below them.