I have checked some gameplay on youtube and the match ends after just one fall. Is there Three Knockdown Rule in this game?
The characters can recover HP/Stamina without use of items after each round?

I've played a bit now in story mode and it seems there's no Three Knockdown Rule, once someone loses all the HP it loses. When the fight reaches 10 rounds it ends and the winner is decided by score. I don't know if in advanced/later stages of the game things change, pretty basic so far.

Stamina do recover in fights, when I want to regain stamina besides the use of item I use a defensive stance, stamina is recovered with time and spend if the guy punches, so fewer punches could mean you regain stamina. Not sure about HP, if it recovers, it's not by much.