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

Regarding transferring troops from an ally during their turn, it's more difficult to reproduce the situation, as it requires an online game.

We launch two instances of Heroes and easily play a network game against ourselves on one computer (a network connection is required). Everything is identical to a game between two computers, except that there can be no disconnections or lag, since the data does not leave the computer and is transmitted quickly.
This is how I test multiplayer.

Calling up the market with a hotkey... sounds a bit worrying.

No more worrying than quickly exchanging armies and artifacts, I think.

Added 12 minutes later
Regarding the bug with underground gates and teleports - it's clear, it's just a new 'ok' [enter] button that shifts the focus to the hero on the right and moves him to the other side, and this causes glitches with duplication. If you press the left 'ok' [esc] after the exchange on the teleport, there will be no glitches.
... We will fix it!

Added 10 minutes later
I've already fixed it, wait for the next version.