Please note that we've updated the Mount & Blade II: Bannerlord save file system which requires you to take certain steps in order for your save files to be compatible with e1.7.1 and any later updates. You can find the instructions here.
Named characters in tournaments do not restore health between rounds.
One hit takes them out in subsequent rounds. I had a random lord in the knocked out position in the final round he was not a part of.