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Does everyone only have access to 2 missions in the introductory Campaign?
Will more missions appear later, or is this it? If this is it, it feels a bit abrupt.

These are introductory Campaigns; missions will appear as you complete them, of course, if you have a licensed version of the game. I can't guarantee anything for pirated copies :smile42:

Added 5 minutes later

I don't think anyone else has had this problem.
I downloaded all the parts using 5 links. I run the self-extracting archive Might_and_Magic_Heroes_VI.part1. The extraction process begins. After some time, the window listing which archives are being extracted simply disappears.

Where did you download it from? If it's a digital version of the game downloaded from the official source, then the problem isn't with the game, but with your system. In that case, I can only suggest the most obvious solution: reinstall the system, although many people would criticize me for that :( If it's a pirated version of the game downloaded from who knows where, then I'm sorry, I don't even know what to suggest.
By the way, it's best to install a system (if you decide to reinstall) that's different from the one you currently have; there might be some damage to the image. I've encountered a similar problem with acquaintances, meaning applications closing on their own. :)