Yes. The Neon Genesis manga gives a unique take on the familiar story, sometimes presenting variations and expansions that add to the overall experience of the franchise.
The Neon Genesis Evangelion manga has indeed finished. It reached its conclusion after a series of chapters and story arcs that wrapped up the plotlines.
Neon Genesis Evangelion's full story is about humanity's fight against the Angels. Shinji is brought into this battle reluctantly. The Evangelions are the only hope to stop the Angels from reaching Terminal Dogma. Along the way, Shinji forms relationships with other pilots like Asuka and Rei. The story also has elements of religious symbolism. For example, the Angels have names with religious connotations. The story gets darker as it progresses, exploring the psychological breakdown of the characters due to the intense pressure of the situation.
Sure! Neon Genesis Evangelion has a manga version. It presents the story and characters in a different format from the anime, but still retains the core elements that made the series popular.
No way. Canonical content in Neon Genesis Evangelion is what was produced by the official studio and creators. Fanfictions, no matter how interesting or popular, are not part of the official lore. 'Lemon' fanfictions, which usually deal with more adult - like or unorthodox relationships between the characters, are completely fan - created and not recognized as official in any way. They are a form of fan creativity, but they have no bearing on the official story of the Evangelion series.