1. For example, when hovering over a hero's portrait, the status bar displays: "Nimbus Necromancer, 859/1500" (it seems like a good and easily implementable option);
2. And I think it would be useful. After all, there are exceptions in the turn order. And visually it would be pleasing, although implementing it would be very difficult, in my opinion.
5. So that battles could be repeated according to the description (by the way, it would be great to save replays, at least in text form, like "Halberdiers (1, 1) - (2, 2)"). Although this is already on the verge of fantasy :)

If the add-on is of high quality, and I think it will be, then over time, perhaps, tournaments will be held for HotA. For example, I am looking forward to it with the same impatience as I once looked forward to SoD.