Floating aquatic plants have spongy bodies to make them light and help them to float on water.
Does roots have cells too?
Every part of aquatic plants have cells too. All cells have a cell membrane, which separates the inside of the cell from the outside environment.
Does this mean, it also protects itself from the cells that get the nutrients to currents aside from the leaves?
Yes because of the presence of lightweight internal packing cells, aerenchyma, including those floating leaves.