Question: Why would Poison Ivy accept several Titan shots from The Joker? She hates him.
Question: In the comic books, animated series, etc, was there a passage connecting the facility to the bat cave like there was in the game? I thought that the bat cave was further away, like under Wayne Manor.
Answer: To add to the answer, Batman tells Oracle that he found the cave after saving an inmate from committing suicide and had secretly been moving supplies to the cave after discovering its location.
Question: Why didn't Arleen Sorkin reprise her role of Harley for Arkham City and Arkham Knight?
Answer: Arleen Sorkin had retired from voicing the character around the time this game was being made. Her last voice role as Harley Quinn was in DC Universe Online, which was released the same year as Arkham City (2011).
Answer: It's not the actual Batcave, it's a secondary location Batman set up in case of emergency. Oracle actually makes a comment along those lines the first time you access it.