HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

And another thing that's still fresh in my memory. During an opponent's turn, the labels indicating the skills of visited witch huts and the spells in magic shrines (and possibly other objects) are inexplicably missing....

And also, as I understand it, all pop-up windows with messages about visiting objects have been removed? The window with the monster animation at the start of the game has also disappeared.

Honestly, I don't understand what you're talking about.
1. Why would I remove all of this?
2. I never observed anything like this during testing (including after reading this report).

Ctrl + down arrow - this function is useful, but I was confused when I needed to detach 5 units from 40 gnolls for another hero to use in a battle in a dungeon (all the troops were transferred, and then everything had to be returned and done again).

I can easily revert to the old functions and assign the new one to Alt, but I don't really want to. I don't see anything terribly critical in their absence. I've been using version 3.0 for so long that I've even forgotten about their existence.
All the other features of version 3 already more than compensate for this, if you can call it a drawback. Is it really necessary to use them so often? Does their absence make the game impossible? Then the original Heroes should be buried, because it lacks not only these functions.