Battlefield Domination

Or any other master in the house
:baby:help nao
1.Can you explain so I can understand
How is battlefield Domination that adds battle round in the battle activated between me and the opponent?
2. How about during siege? As some talent from champs suggest during siege draw …
3. And lastly the 30 min cooldown, how does it works?

And is the champ staying alive during battle and bringing some random amount of extra food contribute to any of the machinations?

Thanks in advance
Kind regards Berto