On the subject of being arrested, I think the process would go like this:
1) When subjects are apprehended they will get restrained, searched and placed in a vehicle for transport. Prisoners would be scanned with whatever on-site security has access to (cyberware scanners, assensing and so on), but in the likely event security doesn't have access to those things they'll assume. That means mage masks for anyone they can't rule out being a mage. Prisoner transport will likely be similar to the enemy prisoner of war
5 S's and a T,
Search,
Silence,
Segregate,
Safeguard,
Speed, and
Tag.
2) Prisoners will be moved to a secure facility (jail) for processing as soon as possible. Once at the facility they will be searched again (stripped, scanned, assensed if possible). Security will attempt to discern the SINs of anyone they have in custody, and create a file for anyone they cannot identify as having a SIN. Any SINs the prisoners have will be checked to see if fake, I'd assume that if this is a Jail, their scans would be rating 6 (or higher). The arrest record would be attached to either the subject's SIN (real one if it exists, fake one if it is not determined to be fake) or to the new file that is created (if no SIN exists).
2a) This assumes the security that apprehends the runners are law enforcement. If it's corporate security, I would assume the apprehending company would do the same basic thing, taking the runners to a secure facility for processing and interrogation before turning them over to the local law enforcement where the process would be repeated. Unless the crime took place wholly on corporate sovereign territory, in which case you'd stay in the custody of the corporation the entire time.
3) Subjects that are deemed threatening (due to offensive cyberware, bioware or magical ability) will be isolated in holding cells prior to interrogation so that anything that can be deactivated will be. Assuming the subjects are in a jurisdiction that have right to counsel, they'll get to meet with counsel before being interrogated (or will waive this right). Interrogators will attempt to discover the depth of involvement in criminal activity on the part of the subject so they can determine what charges will be filed.
4) Charges are filed. This may take a few days, at which time subjects remain in jail. Cyberware is disabled if possible, if not the subjects remain in solitary confinement along with anyone whose abilities can't be "turned off"-- mages, phys ads, and so on. (This assumes that the magical abilities are confirmed, either by assensing or by abilities having been witnessed. Since every jail likely won't have an initiate on staff capable of breaking masking, it's possible an initiate with masking will be released into general population. It's regrettable but there are safeguards in place.)
4a) I would assume that SINs would be scanned many times as a manner of course during this time, basically every time they were referenced. Any SIN discovered to be fake would be invalidated and a new file would be created for that person, assuming no other real SIN already existed.
5) Once charges are filed, bail can be determined. I would assume anyone that is (or technically was) SINless would be considered a flight risk, as would anyone else who would be considered a flight risk on general principles. (Mages are literally a flight risk.) Bail could then be denied for anyone depending on the severity of the crime.
5a) Subjects with unlicensed or illegal cyberware probably won't be released with it. One because it's a crime to have it (which by this point they will already have been charged with) and two because it is evidence that was used in the commission of a crime. Most likely there would be a hearing to determine if the cyberware should be removed, and then the necessary surgical procedures would be scheduled and performed.
6) Subjects who are granted bail and who can pay it would then be scheduled for release. All the necessary information would be attached to their SIN (either existing or newly created). Newly issued SINs are criminal SINs yet, but they will become so when the subject is convicted of a crime. If the subject is found innocent, they still have a normal SIN. (Again, assuming UCAS or similar laws.) I would assume these SINs would have travel restrictions (again depending on the severity of the crime).
7) Trial. Usually months later, the subjects will be taken to trial. They may be tried together or tried separately. Some may be offered plea deals based on reduced sentence foe pleading guilty or for testifying for the state or corporation. After the trial will be the sentencing, the appeals, and possibly a lengthy prison stay.
All this assumes the runners are arrested by a government entity. Characters that are captured by corporations wouldn't have access to a lot of these rights unless the corporation decided it wasn't worth their time and handed them over to law-enforcement. There's also the possibility of jurisdictional conflicts, say if the runners committed their crimes both on sovereign corporate and non-corporate land-- as many running gun battles are.
It's also my understanding that while all of this would conform to the laws of the land where the runners were captured, the entire process is privatized. So while the runners may be subject to government law, most likely they are still being processed and handled by a corporation like Lone Star. (I think Lone Star still retains their prison contracts even in places where they don't provide law enforcement.)