I thought about it for a long time and finally decided to participate in the offline tournament! Hello everyone!! VuzZza is now with you!!

Very nice... it's been a while coming... :D Especially since your clan's rating in offline tournaments has already exceeded zero... so go ahead and aim for first place!

I would gladly play, but there is one problem: the patch won't install, and therefore I have version 3.1((( Can I participate in the tournament with this version?

In principle, you can participate... just don't use any game bugs.
And regarding your problem: what are you doing? And what exactly isn't working?

I want to participate. Sign me up? ;) And I can even say that I am participating, only not officially. I completed several maps from the last Blitz (although not with the best results).

You are already registered for the "Operation Capture" tournament.
And as far as I understand, you are trying to complete the sixth stage of the Blitz Tournament. That's correct!
I recommend that you check out the topic Offline Heroes 3 Tournament Schedule for information about ongoing and planned tournaments!

Also, if you want to play Heroes 1, feel free to join us here.

Sincerely.