Try to make it clear to your players that use of weapons is not OK in a bar fight: have their opponents remove their weapons before the first punch is thrown, and have at least one guard in the bar before the fight starts, although he can just be an onlooker and not take part. If it does escalate and a weapon is drawn or spell is thrown, have the guard step in to break up the fight immediately: it's a good excuse to send them to jail, even if only for the night. If they kill somebody, the consequences should be severe.
And yeah, use the unarmed strike attacks during the fight. The full rules have a mechanic called "nonlethal damage" (look it up on the PRD), but basically this means that taking a character to 0 hp knocks them unconscious, but they don't start to bleed out, and don't need to be stabilised.
Other than that, have the guards show up to stop the brawl at whatever time is most dramatic or convenient. You don't want the fight to go on for too long, it sounds like the consequences of the fight are more important than the fight itself.
For XP, just award the normal XP for whatever CR your encounter works out to be. You can modify this however you want depending on how well the group does: maybe reduce it if they use weapons, or if they get beaten up by the NPCs.
