Questions for the developers:
How will the game be distributed? I mean, will it be possible to download it for free? I wouldn't mind buying it (so to speak, indirectly thanking the creators for their work). I wonder if anyone shares my enthusiasm.

We are working for the idea, and we don't need money for it. The add-on will be distributed completely free of charge.

Will the original Heroes (SoD) be required to install the add-on?

The first beta versions of the add-on will only be installable on them, so - yes. Then - there will be a choice of which installation to download, there will be three types in total:
1. Installation of the full version together with the original Heroes and the add-on itself
2. Installation of only the add-on on top of Heroes III SoD
3. Installation of only the add-on on top of Heroes III WoG 3.58f
Most likely, the first option will be the most popular, now almost everyone has a good connection and downloading 400-500 MB will not be a problem..

And a burning question: will it be possible to disable the commanders (or whatever they are called)?

Of course. Such a global innovation is optional (can be disabled). ;)

Added 1 minute ago

Please, make it possible to disable the terrible commanders!!! :)

Heh, no one has even "enabled" them yet, and you are talking about disabling them. :)