That would be Jack Chalker's 'The Rings of the Master' series.
- They are lead by a (fairly) young Amerind man who goes by 'Hawks.'
- The young lady is actually a creature (who goes by Vulture) created to be able to mimic DNA and thus bypass their security. ("A being who could beat the system at will. Become anyone it wished. Sail through security ports, passing every test—memory, retinal prints, even blood and tissue samples. Gain the full knowledge of whomever it imitated and therefore have full access to anyplace human beings could go.")
- The young girl who must be pregnant (and is blind, in fact) is Song China (or the name she adopts, China Nightingale), a genius, who is saddled with that status to achieve some control over her. (She's the daughter of a high official who basically imposed this on her for being disobedient.)
- The "two people from the prison" could be the Chow sisters (Chow Dai and Chow Mai) who are geniuses in their own right, at least when it comes to bypassing Security systems, if you are referring to the initial prison. They grab/liberate Raven (another Amerind that Hawks knew) and Warlock later, at the prison Melkior, as I recall. In addition, one of the lead scientists, Clayben, comes to join them in book 2.
They are tattooed by a process that is used to basically rebuild people; it can only be done ONCE on almost any being (or, more to the point, on any specific part of a being), so the tattoos are done at skin level, but basically become irreversible.
They all end up stealing a ship; the ship's computer, Star Eagle, becomes part of the team, not to mention developing a very close relationship with China, as she uses a mental interface with the ship to somewhat get past her blindness. They then steal a bigger ship (a Colony ship, basically) from a mothballed fleet, install Star Eagle into it, and go on a quest to retrieve the Rings from various planets where they are held, thence to return and shut off the Master System that is controlling humanity. They do make the inside of the ship into a mimicry of various home environments. Given the volume such a ship is meant to hold, they have all the space they could want.
They also are pursued by Robotic creatures called "Vals" (after Jean Valjean from Les Miserables) that are imprinted with the last recorded memory of the person they are pursuing.
Great books. :)