Re: Question about the initial stages of cells division and differentiation.

First, I am assuming that your question relates to mammalian embryos (in different embryos, differentiation begins at different times) and as you can imagine, the bulk of the work in this area has been done using embryos from the mouse (and other species). Overt differentiation, as reflected in the segregation of trophectodermal and "inner cell masss" cells begins at the 16- to 32-cell (very hard to say exactly when since what is meant by differentiation depends upon how carefully you look, in a sense what you probably mean is "irreversible differentiation").

The experimental evidence is that when you split a 2- cell embryo, the two independent cells give rise to embryos that begin differentiation at the 8- to 16- cell stage. This leads to smaller 'differentiated' embryos than normal -- typically the embryos have fewer inner cell mass cells. (see this page.

Based on experiments of this type, it is thought that the blastomeres count cell divisions and that their internal count is not reset when you divide a 2-cell embryo.