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);

Hmm, and this is a really worthwhile idea. If the add-on is aimed at game balance and equilibrium, then it can definitely be used even in offline mode; so having extra moves will be useful.

- create an "initiative" scale (like in the fifth game);

Regarding the initiative bar, my opinion is - no, this change will completely transform the gameplay in Heroes 3 and most likely not for the better...

- it would be great to save replays, at least in text form, like "Halberdiers (1, 1) - (2, 2)";

Yeah, that would be awesome! It would be possible to share experiences better, create a library with lessons on Heroes 3.

- show the possible damage from spells and unit attacks (so much damage, so many will die);
- display the skills that will be offered, at least for the next three level-ups;
- display the exact amount of gold in chests, etc., resources in piles, monsters in stacks, etc. (at least optionally);
- fix morale and luck, abilities (also optionally);

Hmm, I don't know... you need to be careful with all this... spells and the skill tree are generally good, although I think the authors will have to work hard on it.
But point 3 will definitely lead to cheating! Viewing what and where is probably only for online play, and even then, what will be the point of playing Heroes if you know everything in advance?;)