Merriam-Webster defines anime as "a style of animation originating in Japan that is characterized by stark colorful graphics depicting vibrant characters in action-filled plots often with fantastic or futuristic themes," whilst it defines manga as "a Japanese comic book or graphic novel."
I would think there no question as to whether this were to be limited to Japanese animation or not. Anime and manga are Japanese, so one of the stipulations for asking a question should be whether or not the series is a Japanese production or not.
For example, whilst Æon Flux and Reign: The Conqueror were both conceived by Peter Chung, only the latter was produced by a Japanese studio; since the former was an American production, I would move it not be included in discussions, here.
The Simpsons, Tom and Jerry, etc., are American productions and not anime, so should not be included.
As to the question of whether Chinese and Korean studies should be included, I would again say no, mainly because anime and manga are as much about culture as they are the product itself. For example, Space "Gundam" V has very little, if anything, to do with any of the Gundam series (being more closely related to Macross, which it ripped most of its ideas from), being a Korean production commenced in response to disallowing the real Gundam into Korea.