1. How to check the SoD version

Enter the Heroes windowed mode (press F4 to switch between fullscreen and windowed modes; the color palette should be set to 16-bit: Start -> Settings -> Control Panel -> Display -> Settings -> Color Palette).
In the Heroes window menu, click Help -> About. In the window that appears, you will see the Heroes version.

I already downloaded and installed the patch, how do I check if it's installed?

What patch did you install? 3.2? 4.0? Then, see the answer to your question 1. There you will see which version is installed, i.e., whether the patch was installed.

What needs to be officially installed?

Read the tournament rules in the first post of the thread! Point 2. The tournament is held on Heroes 3: The Shadow of Death version with patch 3.2 or 4.0. :smile35:

Further, I understand that I need to follow the rules, but is there anything else I need to know about leveling up heroes, like not taking Solmyr, and if you do, then after level 2, dismiss him at the end of the day?! Or is it simpler here: download a save, play, save, send, win!!!

No, it's not that simple: download, play. You need to follow the tournament rules, no more, no less. Read them again!