My familiarity with the Batman franchise is pretty much limited to live action stuff. I saw a few episodes of the old TV show when I was a kid (and maybe I just missed the subtleties, but I got the impression Catwoman was a villain like the Joker rather than a love interest as the films portrayed her), and all the movies since the Burton/Keaton films, and I read a novel about a post-apocalyptic Gotham city. Now I'm watching Gotham, and starting to get curious about who's an original character and who exists in other Batman material so as to understand exactly which characters are in any sort of danger. I mostly assumed that anyone with weird powers or gimmicks would be a supervillain in training, but some of them get killed. I also thought the mob bosses from the movies were just made up to represent ordinary criminals to serve as a contrast with the guys like the Joker & Riddler. Except Tom Wilkinson's & Eric Roberts' characters from "Batman Begins" and "The Dark Knight," respectively, have both shown up on the show. The Penguin has the same name he had in Batman returns, and there is a female thief called Selina, like in "Dark Knight Rises," who shares a name if not a profession or backstory with Catwoman of "Returns". There is a hitman in "Gotham' called Zaz, whose name was mentioned by Crane in "Begins", who apparently cuts himself when a target gets away. There was also a girl in the pilot episode whom a lot of online commentators called Poison Ivy, but who did not have the same name as Uma Thurman in "Batman and Robin".

• Speaking of whom, what's Robin's name?
  I thought it was Dick Grayson, as per the TV & Schumacher films, but it was John Blake in "Rises" and I once read a comic book where Robin was checking out Wonder Woman's ass, and she and Batman and Superman called him "Jason". Is he going to have a different name when he works for Ben Affleck in the upcoming movie with those two characters? The obvious explanation that springs to mind is the expected outcome of vigilantes taking children out fighting crime, and I recall a newspaper story about Robin dying, but it's comic books. I saw similar stories about Batman, Superman & Captain America. So do Jason and John and Kelly replace Dick when he gets killed, or do they just keep messing up continuity?
• Is Poison Ivy's name Ivy Pepper or Pamela Isely?
• Are Sarah Essen, Harvey Bullock, Rene Montoya, Chris Allen cops from the regular continuity? I thought they might have been minor cops from the Nolan films, based on the superficial similarities of Bullock and Montoya to cops in "Dark Knight"(the woman being blackmailed and the guy whom the Joker took hostage), but their names were different.
  What about Falcone, Grissom & Moroni?
• Is Jack Napier really the Joker?
  How big a deal is Harvey Dent? I never heard of Two Face before "Batman Forever", but every Batman director has taken pains to cast him. Even though Burton never used that villain, he still put Harvey Dent in "Batman" and cast an actor who was probably more recognizable to juvenile audiences in 1989 than Jack Nicholson.
• Is Fish Mooney new or does she predate the TV show?
• What's the deal with the Riddler? What does he do that makes him dangerous? All I recall of the TV show suggests he's the opposite of a supervillain, sort of like an evil counterpart to Kick-Ass, in that he actually makes things easier for the other side. Sure, it might take a genius with a supercomputer to figure out his clues, but that same genius would never catch him if he didn't leave clues. But if "Gotham" is to be believed, he started out working for the police, which could suggest that he's going to be a kind of Devil's Advocate type of villain who is either an agent provocateur or trying to make a point or else provoke law enforcement to get it right or draw attention to the miserable state of the criminal justice system. Is that his thing?
• What's Alfred's deal? Is he realated to Batgirl? Is he more like the traditional old English butler in the Burton/Schumacher films, or the rough-edged veteran of "Gotham" and Nolan's trilogy?
• What about Rachel Dawes, Vicki Vale, Poison Ivy or Elle MacPherson's character from "Batman and Robin"? Are they actual love interests outside the movies, or is Catwoman/Selena Batman's OTP? Is there any truth to the jokes about Robin (of either gender)?
• Is Gordon's wife named Barbara, like in the Nolan films, or Sara, like in the book? There was a Barbara in the book, but she was not his wife, and also, IIRC, Alfred's niece was Barbara (I thought Harvey Bullok might have been Two face, but Dent showed up on the show, and now there is a second Dick, too). clicking on the character name on Imdb buries you under a ton of stuff all related to Batman, including, apparently, her appearance in that Birds of Prey show that I saw one episode of, and gave up when the heroine got trapped in a sauna and had to strip down. I think she might have more appearances than Jim, actually, so what is her role in Batman continuity? That doesn't track with the stay-at-home mom from the Nolan movies, but then, Zaz appears to be bigger than a one-note mention too.

I'd look this stuff up online, but doing so for other IPs has resulted in spoilers, and if it has been going on for a while (and Batman is at least twice as old as Warhammer 40K, in a lot more media), leaves you looking for a needle in a haystack. If any Batman fans watch "Gotham" I'd appreciate some sort of clarification.