Here is how I have played this stuff works in the past:
Visiting international areas of stationsStations where capsuleers can dock have an "international" supposedly "neutral" area for capsuleers and other visitors. It is supposedly under CONCORD authority, but in practice CONCORD can and does get law enforcement and maintenance help from locals in various degrees. (An Amarr station might have slave janitors, for example)
In addition to ship hangars and corporate offices, this area houses business catering to foreign visitors, varying from bars, cafes and hotels to repairshops and reprocessing services.
This is where visiting capsuleers are generally expected to spend their time. A capsuleer docking on an enemy station and unpodding but staying on this international area is generally fairly safe, as long as they stay out of trouble.
Visiting the parts of a station that are under a nation's sovreigntyWith the exception of the the international area, most of a station is under the owning nation's sovreignty, and there national laws apply. There are checks and customs offices between the two areas, so one can for example get caught drug trafficking if trying to smuggle some personal hangar stores out of the international area.
A capsuleer in good standing with a faction can generally visit safely. (Although having some personal security can be advisable, as would be normal for baselining celebrities) A criminal is a criminal, and an outlaw is an outlaw. That said, especially in low or null sec the locals might not care that much about where one comes from, as long as the capsuleer is not nosy and his money is good.
I play that the capsuleer legal status in areas of national sovreignty is somewhat unclear, and that theoretically a capsuleer can possibly demand for CONCORD intervention if arrested. However, Eve world is clearly a quite dark and corrupted place, and so I imagine theoretical rights and practical rights can differ a lot - demads for CONCORD intervention might "get passed on in due time and with due process" depending on the pleasure of the local authorities doing the arresting. Jita 4-4 chronicle also suggests that "Oops, my gun went off accidentally! How sad!" might be what happens often when local authorities feel like stopping a capsuleer but not like dealing with the associated mess.
And finally, even should such extradition demands to CONCORD make it thorough, I expect CONCORD won't be very keen to strain national relations by forcibly extracting some Don't-you-know-who-I-am?!? who just
had to insist on leaving the designated safe areas and
then proceed to getting themselves in trouble with local law. I figure they will most likely file a query by proper channels, and then accept the answer they get at face value. ("Oh, you don't know where he is? Tell us if you find out, please. Thank you for your time, and pleasure doing business with you!")
I am under the impression major part (if not all) of CONCORD funding comes from the four nations, and CONCORD has not exactly given the impression of being overly concerned over the fate of any single individual capsuleer.
I personally figure the most efficient (and likely safest for the prisoner) way of extraditing such a detained capsuleer would be hefty bribes to everybody even remotely involved - CONCORD officials, detaining local law enforcement etc. Everybody gains something, and if something illegal might have happened, nobody has the motive to go dig it up again.
Visiting planetsI expect CONCORD generally has very little authority over what goes on on planets.
I have played that capsuleer comms implants do not work from planets to space - one needs access to other communication equipment.
This means a capsuleer on enemy planet would be effectively stranded. Too bad for them.