The Bnha universe's reaction would be mixed. Those who are into complex stories, like Todoroki, might study the relationships in Hamilton fanfiction. But others, like Mineta, might not be interested at all because it doesn't have much to do with his usual interests. Overall, it would depend on the individual characters' personalities and interests.
Some would be inspired. Characters like All Might might see Peter Parker's journey as similar to his own in some ways. Both are trying to do good in a world full of challenges. All Might could appreciate Peter's determination to protect his city despite having a normal life outside of being a hero.
For heroic - centric fanfictions, they would likely be disdainful. Since they oppose heroes, seeing stories that glorify heroes would annoy them. They might scoff at the idealized versions of heroes in those fanfictions.
He would probably be quite amused by some of his past antics. For example, his constant pranks on Iruka-sensei. But at the same time, he'd also see the pain he carried from not having his parents and realize how that influenced his actions. He might react with a bit of regret for some of the stupid things he did out of loneliness, but also be glad that those experiences made him who he is today.
One interesting plot point could be Izuku using his knowledge from the future to change certain events in the past. For example, he might prevent some villains from rising to power earlier. Another could be his interactions with his younger self, guiding and mentoring him in a way that speeds up his growth as a hero. He could also have an impact on the relationships between other characters, like All Might and his predecessors.
Obviously, he would interact with his younger self. His younger self is a key character as Izuku from the future tries to guide and influence him. Also, All Might is likely to be an important character he interacts with. All Might has a huge influence on Izuku in the original story, and in the past, Izuku could have a different kind of interaction with him, perhaps sharing future knowledge about threats to hero society. His mother would also be someone he interacts with, as she is an important part of his life.
Well, some past gods might be amused. They'd see these modern interpretations of their stories and characters in the Percy Jackson fanfiction as a strange yet interesting new form of worship or at least attention. For example, Zeus might be a bit irked at some of the liberties taken with his character, but also secretly flattered that people are still so interested in him.
Captain America would probably be very reflective. He might see his past self as a reminder of his long journey and how much he has changed. He could try to offer some words of wisdom to his younger self.
Some characters in bnha scary stories are unique to those stories. These new characters are often created to add to the spooky or suspenseful atmosphere. They might have really strange or terrifying quirks that we don't see in the main series. For instance, a character with a quirk that allows them to manipulate shadows into terrifying shapes that can attack people. So, in many ways, they are different from the characters in the main series.