Because they are disciplined and organized (which almost nobody else in U-town is), they have from time to time served to maintain order there, but only in situations where it would benefit them in some way. Various members have expertise in medicine, construction, wiring, engines, plumbing, and other fields, but those skills are not used except when they will help the Jinx.
Dr. Lee knows a good deal about whatever goes on in U-town, but she keeps most of this information to herself. She sometimes gets interested in a particular person or subject and investigates it quite thoroughly, even to the point of having the Jinx grab specific people off the street so she can ask them questions.
For this reason, among many others, the Jinx are often in conflict with the police, who of course operate in u-town with as few restrictions as everybody else.
The Jinx did not appear in A Sane Woman. They are first mentioned in U-town when CJ (the guitarist who is sitting in with the band Kingdom Come) enters the Quarter, and there is some question about why she is not being asked to pay at the door.
Dr. Lee first appears in the hospital, right before the Battle of the Emergency Room.