The 'clay goo' is the yeast. When it is packaged they put it in some liquid - distilled water, or something. I do know that it is ok to put into the beer. If you could see inside the slap pack from wyeast you'd see about the same sort of stuff, liquid, clay goo and the nutrient pellet.
1 vial is ok for a standard 1.040-1.050 pitch although www.mrmalty.com
has a calculator for pitch rates.
And yes the 1/2 full of yeast is how white lab vials look, a good shake and it all goes back into suspsension.