Well, Syndrome's back story is quite interesting. He started out as an enthusiastic kid with big dreams of being part of the superhero world. He reached out to Mr. Incredible, offering his help and support. But Mr. Incredible didn't take him seriously and sent him away. This was a huge blow to Buddy, who then dedicated his life to proving that he was better than the real superheroes. He spent years inventing amazing technology, from zero - point energy devices to powerful weapons. His plan was not just to defeat the supers but also to create a world where he would be the only one seen as a hero, using his tech - based abilities to outwit and overpower those who once rejected him.
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.