That’s exactly what I was looking for and couldn't find; there must be different names...

No, they are here.

And another question: how do you extract a video from the mod, embed it in the map, and make it play at the beginning of the map?

You need to extract all files from the dialogue scene... But where to get them – you need to look in the scripts: there should be a link to the main file of the dialogue scene, and from there to all other files.

Is it possible to create your own hero with their own special specialization? For example, an ability to turn vampires into Death Knights for an additional fee? The idea is taken from Heroes III, where a companion hero turned Elven Archers into Snipers.

Set the specialization to zero and then use scripts. However, such a specialization as yours needs to be thought out first from the point of view of the interface: how will the conversion be carried out? Automatically? If so, under what event? With any change in the army? When entering a city? Once a day? Is partial conversion possible, and if so, how? One creature at a time? Or a large dialog that allows converting 1, 5, 20, or 50 creatures at once, for example, depending on the selected item?