If we take two nearly identical cells, differing only in genetics, from two different organisms from the same species, say, a basic skin cell, and subject them to stimulus X which causes them to divide, is it possible that due to genetic/epigentic factors they divide at different rates? Is it possible for one of the two cells to be innately more receptive to the stimulus? Lastly, what would cause the cells to stop dividing? Do they simply keep dividing until they've reached a mass where they die as fast as they divide and so cant grow any larger? What natural causes in the body prevent reaching this equilibrium (if it exists) or rampant cell division (if it doesn't) provided the stimulus is always present in the body?

Different cells will divide at different rates and respond to stimuli differently. There are again a number of genetic and epigenetic factors which will determine when the cells stop dividing. Have a read of this about human cells:
https://en.wikipedia.org/wiki/Hayflick_limit