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

Generally speaking, we usually don't have any restrictions, and I don't know if anyone will insist on them (AC or HW). All restrictions are set on the maps, such as banning the Ring of Permanence, Gloves, Boots, and unwanted skills (stealth, resurrection, and others).
On some maps, there's a long-standing 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.