I've never been in a fight so i don't know exactly how it works, but I don't think its to the death. I've never heard of a player being beaten to death. Healing occurs over time or through a medical facility, but I don't think that has been implemented yet. Just don't get into any fights for a month or so and see if you heal. :)
You fight until you beat the brawler, or your character reaches one health point.
Healing occurs naturally over time. You can also use a healer NPC (if you would have one, that is) who charge a small amount of credits to heal.
Yep, you always have the option to run away. But if you continue to fight, it will be until either you or the brawler reaches 1 HP, whichever happens first. At no point will either of you actually die. ^_^