What exactly happens to the yeast when they are in the keg? Does it kill it, over time? Force it to the bottom? What does the pressure in the keg do to yeast?
It all depends on how much pressure and where the yeast is in it's life cycle. Serving pressure in the keg doesn't have much effect on the residual yeast at all.
Lower pressures (<15psi) are generally considered beneficial during active fermentation. It slightly increases early diacetyl production, but also increases late diacetyl consumption by the yeast. It decreases production of esters, fusels, phenols, and a host of other things that are generally considered flaws in most styles. It allows higher fermentation temps without the associated off flavors, or allows for a "cleaner" beer at normal fermentation temps. Not good for belgians or other styles where the esters and phenols are a large part of the style though.