A great villian back story often involves some form of trauma. For example, they might have been bullied or abandoned as a child. This can lead to feelings of anger and a desire for revenge. Another key element could be a thirst for power. Maybe they grew up in a powerless situation and saw power as the only way to get what they want. Also, a sense of being wronged by society can be part of it. If they were discriminated against, it can fuel their villainous actions.
In these fanfictions, a common theme is the exploration of the grey areas between good and evil. Bella as a villain may not be entirely bad; she might have her reasons for her actions. There could be themes related to moral ambiguity, where her actions are not clearly right or wrong. Additionally, the theme of identity crisis can be present. As she becomes a villain, she may struggle with who she is now compared to her previous self in the original story, and this internal conflict can drive the plot forward.
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.