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

... By the way, regarding this, a question: How important is the chat window during the exchange phase? It wouldn't be a problem if part of it is displayed over the character portrait of one of the heroes.

For online players, the chat window during the exchange phase is not needed at all. It's a waste of game time. Communication usually happens at the start, and also when a player is waiting for their turn or is in combat.
However, aspects related to saving game time are interesting.
Could it be possible for the turn timer to start after a turn is taken (and the 'Ok' button is pressed in the notification window), rather than as it is now - where the time runs independently? Also, there are moments when, in the last second, you gain experience from a Pandora's Box or another event, but there is no time left to choose a skill when leveling up; everything is done automatically.
Could it be possible to set the turn time in the settings - 3 minutes, 5 minutes?