Correct, there's two sections: The capsuleer section (that's basically what it's called) and the baseliner section. Both of these terms are slang -- they don't really have a "formal" name.
I presume I should think of this side of the station to be run like an aircraft carrier the size of a small planet?
No, this side of the station would be run like a closed community for celebrities. The best in finery and comfort: very rich, with the best service, and it keeps the riff raff out. But yes, it is policed by CONCORD, unlike the rest of the station. It is specifically for capsuleers, not pilots in general, and is held to CONCORD capsuleer laws rather than the local nation's laws.
In the Pilot area where there are hangars and docking bays, I presume there is a Station Commander? Flight Control Officer at least an officer on deck?
I wouldn't consider the hangars part of the capsuleer section, though certainly capsuleers get access to premium berths, and can disembark straight from there to the capsuleer section.
Each capsuleer would probably maintain their own deck chief in charge of managing their own ships and inventory.
We don't know exactly where station administration might be. It could be in the baseliner section, or it could be in the capsuleer section. There might be one in each, separated between the people running most of the station and those specifically catering to capsuleer interests (because, again, capsuleers get preferential treatment).
There would be crew rota's and even a recruitment process in-station to find and vet good replacement crews.
I agree there would be recruitment work done on station. This would probably be a global recruitment pool that operates across the entire cluster (considering how much of an industry it is). Capsuleers would probably finance/recruit from that rather than doing their own individual recruiting efforts.