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.
One great 'Batman Begins' and 'Dark Knight' fanfiction is 'The Gotham Reimagined'. It delves deep into the backstories of the characters, giving new perspectives on Bruce Wayne's journey. It combines elements from both movies in a really interesting way.
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.
Perhaps a plot twist where Bruce Wayne discovers that his father had a secret life as a crime - fighter too, but in a very different way. It could change Bruce's perspective on his own mission and add a family - related mystery to the fanfiction. This could involve finding hidden journals or messages from his father that lead him in new directions.
One great example could be a fanfiction that explores Bruce Wayne's internal struggles in more depth between the events of Batman Begins and The Dark Knight. It might focus on his relationships with his allies, like Alfred. Another could be a story that delves into the Joker's origin from a different perspective, perhaps showing how he came to be in the criminal underworld before his encounter with Batman in The Dark Knight. There are also fanfictions that might imagine alternate endings to the events in these movies, such as Batman finding a different way to deal with the chaos the Joker creates.
Batman Begins tells the origin story of Bruce Wayne. He witnessed the murder of his parents as a child, which deeply traumatized him. This event led him on a journey to fight crime. He trained with the League of Shadows, learning various combat and stealth skills. But he ultimately rejected their extreme methods. Returning to Gotham, he used his family's wealth and resources to create his Batman persona, with the intention of cleaning up the crime - ridden city.