Most likely not. While the idea of exploring different relationships in fanfics can be creative, a 'gay fanfic' of 'The Incredibles' might have content that is not suitable for the general audience. For example, it could involve sexual undertones or re - interpretations of the characters' personalities in a way that is not in line with the family - friendly image of the movie. Also, in some communities, any form of same - sex relationship exploration in fanfics can be a controversial topic.
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.