Only Azyl installed correctly; everything works fine there. But with all the other mods, only the appearance changes, and that's it. Right now, I'm playing Heroes 5 with the Armageddon's Blade mod – it doesn't have any other mods. If we consider the logic, why does Azyl install normally, while the others only change the appearance? And the other game is Heroes 5 with mod 5.5; it has other mods, but they only change the appearance as well.
It has a file called MMH55-Index.pak.
This file contains folders, and in the \GameMechanics\Creature\Creatures folder, there are folders with the characteristics of the units. Delete them, and the units will change in the cities.
In the same file, there's a MapObjects folder – it contains the heroes.
Generally, I just open the mods and compare the contents of the folders to find conflicting files.