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.
Naruto could find some similarities between his own values and Batman's. Both are determined to protect their respective worlds. However, the storytelling style in Batman fanfiction might be a new concept for Naruto. He may enjoy the complex characters and the dark, gritty atmosphere often found in Batman stories, or he could be put off by it as it's so different from the more straightforward good - vs - evil in his own world.
One interesting 'batman reaction fanfiction' story could be about Batman's reaction to a new super - villain in Gotham. The villain might have a unique power that challenges Batman in ways he hasn't been before. Another could be his reaction to a new Robin joining the team. Batman has to adjust to training a new sidekick and protecting them while they learn the ropes.
One interesting 'Batman Arkham Knight' reaction fanfiction could be about how the citizens of Gotham react to Batman's final showdown with the Arkham Knight. It might explore their fear, hope, and the impact on the city's future.
A good Spiderman vs Batman reaction fanfiction should have well - developed characters. It should stay true to the essence of both characters. For example, Spiderman's quippy nature and Batman's brooding seriousness. The plot should be engaging, not just a simple fight. Maybe there could be a misunderstanding that leads to the conflict. And the setting can add a lot to the story too. If it's set in a shared universe where both heroes have to deal with new threats while also facing each other, that could be really interesting.