Why they the sample from the mouth instead of simply looking at sperm or egg cells.

A reproductive -sex- cell. In females, egg; in males, sperm

Hope that answered your question...

Liquid water is less dense than frozen water. (you can see that when ice stays above water in your cup.)

The reason for that is that when water freezes it’s molecules position further away from each other(because of the 4 hydrogen bonds and the honeycomb shape that ice gets). So the volume increase and density decreases. (Density=mass/volume).