Well, one possible plot could be Percy and Nico having to deal with typical high school problems like bullies. Percy might use his water powers in a discreet way to stop them. Nico could be the mysterious loner at first but then make some real friends as he shows his cool powers. And they might also have to hide their demigod identities from the normal students.
In a fanfiction where they go to high school, Percy would likely be popular for his heroic deeds and good looks. He might join the swim team and break all the records. Thalia could be the cool girl who rides a motorcycle to school and gets into trouble for parking it in the wrong place. Nico would be the mysterious new kid. There could be a plot where they have to team up to stop a monster that is lurking in the school basement.
A powerful monster from the demigod world that has a vendetta against Percy and Nico could be the main antagonist. It disguises itself as a teacher or a student and slowly starts to manipulate things in the school. It tries to isolate Percy and Nico from their friends and then attack them when they are at their weakest.
Well, perhaps Percy and Nico could be transferred to Hogwarts through some sort of magical accident. Maybe they'd have to deal with the different magical system there compared to their own world. They could make new friends among the Hogwarts students and get involved in the typical Hogwarts adventures like the Triwizard Tournament or dealing with a new dark threat.
In highschool fanfiction, their relationships could develop in many ways. Percy and Nico could bond over their shared experiences of being different. Percy might help Nico come out of his shell and make more friends. Thalia would be like an older sister figure to both of them. She would protect them from any mean - spirited students. As time passes, they would have sleepovers at each other's houses (or cabins in Percy's case), and during these times, they would share stories and secrets, strengthening their relationships.
In this kind of fanfiction, they might face challenges adjusting to the new magical environment. Percy could be confused by the different types of magic in Hogwarts compared to his own demigod powers. Nico might struggle with the more structured and rule - bound nature of Hogwarts. Thalia could find it interesting but also be a bit rebellious against some of the Hogwarts traditions.
If Percy and Annabeth were to go to highschool in fanfiction, it would be a whole new world for them. They are used to the dangerous and magical world of demigods. At highschool, Percy might get into trouble for his impulsive nature, but his loyalty to his friends would also make him popular. Annabeth would be the girl who always has her nose in a book, yet she'd also be the one everyone turns to for advice. Their relationship would also develop in new ways, perhaps facing challenges from normal high school romances or jealous classmates.
The camp leaders might betray them. If there is a power struggle within the camp, and Percy and Nico are seen as threats to the current leadership's power, the leaders could set them up. They could make it look like Percy and Nico are breaking camp rules or endangering the other campers, which would lead to the rest of the camp turning against them.
They would surely meet Harry Potter. Harry could be curious about their different magical abilities and background. Hermione would also be there, probably peppering them with questions about their own world's magic. Ron might be a bit skeptical at first but warm up to them eventually.
Yes, there are many. You can look for ones on platforms like FanFiction.net. Just search for 'Percy and Nico friendship' and you'll find a lot of great stories that focus on their bond as friends, like adventures they might go on together or how they support each other in the face of challenges.