Cell differentiation by non-identical copies
I found a partial answer to my and this question at Quora:

What regulates initial cell differentiation?

Ian Driver says:


  In many organisms the initial cell has mRNA (or protein) partitioned
  in one half of the zygote.  One daughter cell inherits most of the
  mRNA or protein and goes on to activate or repress genes in that cell,
  but not in the other.  This has been visualized and well studied in C.
  elegans: Asymmetric cell division and axis formation in the
  embryo.