Is the new Gotham TV series considered to be canon for Batman?
The TV show introduces plenty of known characters from the get go (Jim Gordon, Bruce Wayne, Alfred, Catwoman, the Penguin, Poison Ivy). Are all these characters and stories to be considered canon? Or is this more of an alternate universe timeline?
The short answer: It is its own canon, just as nearly every Batman that came before it.
The long answer: Batman is one of the most prolific DC characters to date, and has had numerous different interpretations. You can read more about them here. Unless otherwise stated, these each fall into their own separate canon, including:
Batman Comic BooksThe DC Comics/Detective Comics canon for Batman spreads about as far and wide as comic book history itself, has had numerous spin-offs, and has changed multiple times.
Batman TV SeriesThe original Adam West TV show, which spawned its own movie.
Tim Burton Batman Movies & Sequels+Includes the original Tim Burton's "Batman", "Batman Returns", "Batman Forever", and the now-infamous "Batman & Robin".
Chris Nolan's Batman MoviesIncludes the new series of Batman movies, including "Batman Begins", "Batman: The Dark Knight", and "Batman: The Dark Knight Rises", as well as a direct-to-video animated feature "Batman: Gotham Knight".
The DC Animated UniverseConsists of numerous DC Cartoons, notably from Batman's standpoint "Batman: TAS", "The New Batman Adventures", "Batman Beyond", "Justice League", "Justice League Unlimited", and a number of cameos in other animated series.
Arkham Series Video GamesMost video games are one-shots that are derived from other works and don't connect to any other series, but the Arkham series of video games is notable for having its own continuity, including "Arkham Asylum", "Arkham City", "Arkham Origin" and "Arkham Knight".
The live-action show "Gotham" falls outside of all of these canons. Though what all of these canons share in common is that they are based off of the previous works. As pointed out by Richard, it is the artist's discretion which source to follow when writing new material for a separate canon. So it is well within the liberties of the show to introduce new characters.
+As pointed out in the comments, Tim Burton had nothing to do with Batman & Robin specifically.
The Batman universe spans a couple of dozen different comic series, eleven feature films, twenty animated films and nine TV series.
There is simply no agreed canon between these different properties. Although Gotham uses the licensed characters found in the other Batman serials, it's generally at the discretion of the Director and studio which elements to preserve and which to ignore.
Here's the thing I tell my friend when he starts asking me if something in a comic based show or movie (be it live-action or animated) is canon. It is its own entity with its own history and versions of characters. No two versions of a character will or should ever be the same as the original source material, nor should the world be held to those restrictions. So Gotham is canon for whatever future they want to tell. Their Batman and Gotham and criminals will be very different than what we've seen. For example, Penguin and Riddler will be middle-aged men when Bruce dons the cape and cowl. That automatically changes the dynamic. Penguin was older in "Batman: Earth One", but he was also the Mayor. So yeah changes happen.
No, Gotham is not in any established canon. The creators within the last week have said that any character could be killed. There's no way that if someone like Edward Nygma (for example) gets killed in season 2 that it could be a part of canon.
I would agree it is its' own canon. In the comics, Barbara Kean was Gordon's first wife. Assuming they are not throwing out another double-cross, they are definitely messing with Joker's origin.
