Test your knowledge of Heroes of Might and Magic III.

Nestor86, although, upon reflection, your question becomes clear, but in the future, could you please express yourself more clearly?;)
I think that in both cases the answer is negative; they don't have an effect, because specialization in creatures only gives them bonuses to attack and defense parameters, and special abilities (double damage and deadly gaze) do not depend on them. This is if we reason logically. But in practice, I haven't tested this and don't know if it's true; the game developers may have added some additional bonus to the creatures that is not described in the documentation. Only someone who can analyze the relevant sections of the game's source code or has encountered a clear manifestation of the enhanced abilities of these monsters with these heroes can say for sure.