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Colleagues, regarding running the game in a window: google the program DXWnd — it's simply an epic tool with hundreds of settings (though you'll have to spend some time configuring it and figuring out how it works). You can run Heroes in a window, and most importantly! — the game will remain active even while in the background if you switch to a browser, for example, while the computer is taking its long turns in-game.
Usually, games pause if you Alt+Tab to another window.
(I'm writing this post right now, and there, in the background beyond the browser, the computer in Heroes is making its moves on a huge map!)
There is also a program called D3DWindower — but it isn't as flexible; it's very simple and has own unfixable/unconfigurable glitches.
Added after 7 minutes
Chapaev1
-yes, you just need to use the process of elimination, gradually removing maps and mods from the Mods\Maps folders — and at a certain point, the glitches will disappear, and the culprit will be identified. The thing here is that any user-made (amateur) map can (is allowed to) change or disrupt the normal operation of the game.
Added after 5 minutes
Folks, here is the link to the DXWnd program, with a googled help file (English) included:
https://yadi.sk/d/KSyDDwOxufthD