If you go back to the times when bonds and obligations were common (in England, for example), it really did come down to "don't commit crime/'disturb the peace' or else you shall have to pay a fine of [predetermined value]. Please sign here.". Holding good behavior for ransom. It seemed to work, too.
Now, granted, that was conducted by monarchs with a very, very strong interest in law and order (particularly post-war of the roses), rather than by megacorporations with an interest in profit margins. However, I could see such a system being a reality in the cyberpunk people-as-human-resources world that is the Caldari State.
Oh, certainly-- but that was backed up by some very straightforward and widely understood law that those contracts provided some refinement to. That was a period where most of the out-and-out law was so obvious that your average peasant understood it in detail-- you don't commit theft, you don't commit murder, beating your spouse is fine, and a contract is a contract. That last one is probably responsible for a lot of our images of demons doing deals with mortals-- there's more than one medieval con artist who got rich cheating people with viciously-written contracts. It's one of the places our limits on foreclosure come from.
It's entirely possible that the Caldari legal code is derived almost wholly from contractual agreement-- but I also suspect that the system has gotten pretty well refined and streamlined over time.
When the belligerents walked into the bar, they likely walked by a sign/terms of use that likely included "do not physically assault the other patrons, belligerents will be barred from all Ishukone bars for the following month."
Considering the Caldari, and especially Civire, cultural tendency towards violence, I'd put the ban at one week (possibly much less) and apply it only to that specific establishment. If it goes past that, it's probably not enforced-- and thus broadly ineffective.
The Hyasyoda crew member may or may not have recourse to report his assailant to station security, depending on the contract Hyasyoda has with KK and whether or not he is even allowed to talk directly to the Home Guard security team.
I suspect station security has blanket license to keep the peace, but yes, that sounds about right.
The dock-worker, as part of his employment contract, subjects himself to KK's jurisdiction and may have violated the contract by assaulting a agent of a client, possibly causing KK to have to pay Hyasyoda reparations since one of its employees violated the contract. KK, not being to happy about this, docks the dockworkers pay, restricts his services privileges, and possibly re-assigns the dock worker to one of many asteroid mining sites (which rumor has it are prone to being attacked by pirates/capsuleers).
Okay, here's where you lose me. The Caldari are not so warm and fuzzy as to give a damn who struck whom unless it led to a major incident. I can see each group being responsible for its people's conduct, but remember also the way the Caldari culture works: life is a test; the strong survive. Bearing in mind, again, the undercurrent of violence in Civire culture, fights are probably too common for corporate higher-ups to take them very seriously. Unless somebody was rendered unfit to work, I doubt the corporate higher-ups care; having medical patch up some cuts and bruises is just a cost of doing business.
So ... that was maybe an unfair example-- likely jurisdiction in a minor assault between worker-caste equals: nobody's interested. It might not even be a crime.
Striking an executive, on the other hand....
Considering the Caldari fondness for hierarchy, it strikes me that most Caldari courts (certainly the ones handling petty theft and such) are probably run by a single magistrate and handled as bench trials. Below a certain level, bringing an attorney in might well be either "not done" or forbidden outright; the magistrate hears each side's story, rules on the facts, and hands down a decision and any appropriate sentencing.
Higher caste and higher crimes might involve larger tribunals and bring lawyers into play, but I'd be surprised if the megas felt the need to hire a lawyer for every unskilled laborer who went a little too far in an argument and landed his cousin in the clinic for a week.
Which brings up the question of - are there prisons?
"Methods of Torture: The Caldari" suggests that there's more than one kind of prison. Those who transgress can be ... modified. Not controlled, necessarily, just creatively damaged. Note that the protagonist/victim in that story is a white-collar petty embezzler, though.
Probably, there are actual prisons in places, though it's also quite likely that many serious crimes carry a penalty of revoked citizenship upon conviction ... after which the revenge any aggrieved party takes is no longer the business of the law.