In English the word "manga" is used to refer to Japanese comics. I would like to know if this word is similar to "anime", where westerns use it only for "Japanese" animation (in a broad sense since several "Japanese" animations are produced in Japan but animated on Korea or other country) or does it mean comics in general? Is a fanfic japanese comic a "manga" or does it have to be paid and officially released to be "manga"?
漫画/マンガ in Japanese is close to comic in English. It's a generic term that safely includes, for example, Peanuts and Spider-Man. It doesn't have to be released commercially, and even a 10-year-old boy can draw 漫画. It usually consists of many pages and frames (コマ), but when a picture has a balloon and a "story", people sometimes call it a (1コマ)漫画.
アニメ also is a word that includes foreign cartoons such as Disney's movies.
Manga has a much broader meaning traditionally. For example, every year Hokusai, the Japanese artist, would create a sketch book of drawings in response to his students constant question of “what should we be drawing?”. I have that multi-volume set at home. Hokusai drew every aspect of Japanese culture and society of his day as well as imaginary creatures. Not a comic book at all.