How to get the girls into your cells in your living quarters? and how to unlock more heroines?
Go to your lab, select devices, select upgrade devices, and then up grade them all the way until the "Unlock" button in the middle lights up and press that and upgrade it one last time to put them in the cells (as of now, you can't do this for Black Canary, Hawk Girl, Zatanna, or Huntess yet). While in the cells, heroines can't be used as strippers or put in the bordello. You can reset their devices to allow it again, but that takes them out of the cells and completely resets upgrades so you have to pay for all of them again.
To get more heroines, first capture the starting three, then talk to Tala in her workshop for a sidequests to unlock the capture of Wonder Woman, Vixen, and Zatanna and talk to Roulette in her office in the Glamour Slam for Hawk Girl, Super Girl, Star Girl, and Miss Martian. After the Bordello is built, talk to Cat Woman in her office in the Bordello for Starfire and Artemis. After you've captured all 12, the option for Terra will unlock with Cat Woman. You can also capture Raven through Tala by selecting the Summoning option in her workshop and doing the subsequent side quest (Raven stays at Tala's workshop in one of it's rooms rather than Lex's hideout).
There are several other characters you can get, mostly henchwomen. Harley you get via Joker events prompted at the Legion HQ, Lois via the Daily Planet after raising your threat level enough to get a warning about her, Superwoman through a Parasyte prompted event at the HQ after meeting Grodd, Audrey via some Vandal Savage events at the Glamour Slam, Blackfire via some Lexcorp office events after getting Starfire, Cheshire randomly when visiting your defenses, Galatea via a Star Labs heist (I forget the exact circumstances, unfortunately), and Killer Frost via some Glamour Slam events after breaking her out of prison (which you can do via your office after the Prison event). Most of these prompt via RNG, so just keep visiting those places each day after fulfilling the requirements.