Why we need an egg cell donor and a surrogate mother in an organism cloning process?
Could a whole set of artificial organism-cloning process only be
  operated on a somatic nuclear donor?


No, this would not be possible. Single-cell reprogramming would enable you to reset the potency status of that cell up, yielding an embryonic stem cell (ESC). However, ESC do not have the ability to generate extra-embryonic structures (e.g. placenta), which are known to be required for providing oxygen and nutrients to the embryo, amongst other relevant functions.

Theoretically, it could be possible to replicate the embryological environment, and I think this is the second part of your statement. Nevertheless, in practice this is not possible... the amount of signals and parameters that one would need to control simultaneously is far too extensive.

I don't quite see the point of having an enucleated egg and performing somatic cell transfer, when you're not really interested in implantation in utero. Somatic cell reprogramming would be sufficient (see iPSC)