Well, Bakugo might scoff at first. He'd probably think Batman is too brooding and not as straightforward as he likes his heroes. But then as he reads more of the fanfiction, he might grudgingly admit that Batman's detective skills are cool. Deku, on the other hand, would be super interested. He'd be analyzing every move Batman makes in the fanfiction, taking notes in his head about Batman's strategies and how they could be applied in his own hero work. Uraraka would be more focused on the relationships in the fanfiction. She'd be all 'aww' at the cute moments and feel for the characters when they're in trouble.
Nezuko is initially 12 years old in the manga. As the story unfolds, her age doesn't change significantly in a traditional sense, but her character development is quite remarkable.