An online tournament for Heroes 4 is planned in collaboration with Heroes League.

We'll be waiting (but it would be good to know in advance. Are there any restrictions like in Heroes of Might and Magic III? For example, is there a ban on building a guild if you find a high-level scroll?

Generally, we don't have restrictions. I don't know if anyone will insist on them (AC or HW). All restrictions are set on the maps, such as banning rings of permanence, gloves, boots, and other skills (stealth, resurrection, etc.).

On some maps, there's an old agreement to restart if a lord starts as the hero when playing as Haven, but this isn't a rule, but rather a habit. In most cases, you can play that way too.

What are the tournament dates? Does that mean it's no longer in January?

Why not? There are still more than two weeks left until the end of January. :)