It contributes by giving fans more content. Fans are always hungry for more stories about their favorite characters, and the fanfic satisfies that need. It also allows for a wider range of voices in the fandom. Different writers can bring their own ideas and perspectives, which enriches the overall discussion and enjoyment within the Incredibles community.
One interesting plotline could be the further exploration of the family's relationships. For example, how the kids deal with growing up with superpowers in a world that still has some prejudice against supers. Another could be the origin stories of the villains in more depth, like Syndrome. Maybe there could be a fanfic where he had a chance at redemption.
The Avengers would likely have a range of reactions. Captain America would respect the Incredibles' sense of justice. And the Hulk might just be confused at first but then find it cool.
If the Avengers watched The Incredibles, it could be a very interesting scenario. The Hulk might get a bit jealous seeing Mr. Incredible's strength at first. Black Widow would notice how Mrs. Incredible manages to be a great mother and a superhero at the same time. Hawkeye would be interested in the archery skills of any character in the movie who might use a bow. And they all could learn something about teamwork from the family's dynamic in the movie.
No. Since it's a 'lemon' fanfic, it likely contains inappropriate content. 'The Incredibles' is a family - friendly franchise, and a 'lemon' fanfic would go against the intended audience and values of the original work.