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.