Where does energy come from in a nuclear fission if nucleon count doesn't change? In a nuclear fission the total number of protons and neutrons are conserved. Then the mass converted to energy $E=mc^2$. From where this mass come from? Does that mean that all protons and neutrons are not identical in mass.
 A: Have you ever wondered why do the protons and neutrons stay together in the first place?
These particles are bound to the nucleus by attracting forces (strong nuclear forces) which I won't dwell into in this answer rather I shall speak in terms of energy. There exists energy of interaction, called binding energy, which keeps the nucleons together.

The nucleus as a whole has a lower potential energy than their individual particles held separately which implies that you need to supply energy to disintegrate the nucleus (which is why a moving particle, usually neutrons, are bombarded with the fission reactant to initiate a non-spontaneous nuclear reaction; the moving particle has kinetic energy). Notice that the nucleus is lighter than its constituent elements. As you said, energy and mass are interconvertible. The missing mass takes the form of binding energy (assuming that other forms of energy of the nucleus and the constituents are zero).

The mechanism of a non-spontaneous nuclear fission reaction can be described in very simple manner as follows.
Moving particle bombards the fission reactant's nucleus and transfers the energy to the nucleus. The nucleus begins to waggle and at one point (unless the newly formed nucleus with the bombarding particle is stable) it breaks apart into two or more pieces. 
The new products have different binding energy. This difference in binding energy is the energy which is released from the reaction (in the form of kinetic energy of the products).
The above mechanism is highly simplified and lot of complicating factors have been ignored from the above mechanism.
