Not exactly. Batman Begins is one interpretation of Batman's origin story, but it's not the definitive or only 'real' one. Different Batman stories and adaptations offer various takes.
Yes, Batman Begins can be considered a mystery fiction to some extent. It has elements of mystery as Bruce Wayne uncovers secrets and faces hidden threats in Gotham City.
In Batman fanfiction involving Pretty Poison, it often explores the complex relationship between Batman and this villain. Sometimes, it might focus on Batman's attempts to outwit her devious schemes. For example, he has to figure out how to counter her poison - based attacks and manipulations in the city of Gotham. This can lead to some intense and thrilling storylines where Batman's detective skills are put to the ultimate test.
Poison Ivy can also be a character of redemption in some fanfic. Maybe she realizes that her extreme methods are not the best way to protect the environment. She could then start to work with Batman or other characters to find more sustainable solutions. This would be a different take on her character and could lead to some really interesting story arcs in the fanfic world.
The appeal of Batman and Poison Ivy in fanfiction lies in their contrasting natures. Batman is all about order and justice in Gotham, while Poison Ivy is more about nature's chaos. This contrast makes for great storytelling as it creates a natural conflict. Writers can play with this to create unique and engaging plots.
One idea could be that Batman, in his quest to fight crime in Gotham, discovers some sort of interdimensional rift that leads him to the world of The Avengers. He then has to team up with them to stop a common enemy that is using technology from both universes to cause chaos. For example, Loki could be teaming up with some of Batman's rogues gallery like The Riddler to create complex puzzles and illusions that are both magical and technological in nature.