Canon refers to accepted mythology, or history. Fan fiction is not a part of the official story, so that would be considered non-canon.
Manga often loses something in its adaptation to anime, so it can be said that manga has its own canon, and the anime another.
However, unless something in the anime absolutely contradicts something in the manga, there really is no reason to suppose that something mentioned in the manga didn't also happen in the anime as well, just because it was not expressly seen. It can be rationalized that it just happened off screen.
Generally, an anime is a team effort of talented people who base what they did on the manga, but they aren't bound to follow it 100%. The manga, however, is 100% the work of a single artist/writer, so it will always best convey its creator's intentions.