Xaart, here's a suggestion: was your game installed from a licensed disc? If so, it seems that not all files are written to the hard drive, so when the game starts, it requires the CD, from which the remaining files are loaded during the game (the only form of copy protection in "Heroes 3"). If so, there is a special "No CD/DVD" option in the HD mod (on the right on the starting screen). Or (but this is more complicated) you can install a version of "Heroes" where this is already done (a repack, I have one).
As for the resolution, you can quite normally play at 1024x768 (I played in this mode even with my old CRT monitor), but, of course, the higher it is, the better: most of the map is visible without scrolling.

Marmot, good afternoon! Yes, the game was installed from a licensed disc, I play from a virtual drive, with a full-screen view. In Era, the "no CD/DVD" option is enabled by default. I once installed the HD version of the game (not the HD mod), but I didn't like it, as it didn't recognize most of the maps that were easily launched on my outdated version, and my monitor didn't support the resolution. I uninstalled it and don't regret it.

In Era, there were also old maps, I deleted them all and replaced them with my own. However, I discovered many new features that I hadn't noticed before. Plus, there were some amusing moments. To check, I started a game with the Inferno starting castle. What amused me was the behavior of the neutrals. For example, if there is a group of 10 Gogs, one of them joins, while the others resist. Hmm... usually it's like this: either they all join, or they are hostile, engage in battle, or flee. But here there are 50 shades of gray)).

Added 6 minutes ago

Does it crash with the HD mod? There are at least 4 launch modes by screen + screen resolution selection (to make all functions work, the resolution must be greater than 1024x768). But if a resolution higher than the screen allows is selected, or an unsuitable image mode - the game will simply crash when loading. Therefore, you need to select a suitable mode and resolution when starting (experiment).

Hi!) No, it doesn't crash, everything works in HD Mod Era II. I just installed the HD mod, the link to which Marmot posted, but it refused to work.

I figured out the resolution and chose the most optimal one. Unfortunately, my monitor isn't even HD ready, I definitely need to get one that supports 1080p.