One common theme is friendship. Percy's overprotectiveness can be seen as an extreme form of his friendship with Nico. He wants to keep Nico safe from the various threats in their world, which shows how much he values their bond.
One place to start looking could be Archive of Our Own (AO3). Just search for 'percy is overprotective of nico' in their search bar, and you'll likely find a good number of relevant fanfictions.
Well, it could be that in the context of the fanfiction, Clarise has a deep understanding of the threats Percy faces. She may have witnessed some near - misses or had premonitions about his safety. So, she becomes overprotective to prevent any harm from coming to him. Also, it could be related to some unspoken bond or connection they share within the story's unique plot.
Maybe Clarisse has her own reasons. She might see Percy as someone who needs protection in the complex world of the fanfiction setting. It could be that she has a soft spot for him deep down, or she feels a sense of responsibility towards him for some unspoken events in the story.
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.
One common theme is friendship. Percy's overprotectiveness often stems from his deep love for his friends. For example, he doesn't want to see them get hurt during battles or dangerous quests.
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.
One great fanfiction could be about their adventure in an unknown magical realm. They might have to combine their unique powers - Jason's control over the winds, Nico's ability to summon the dead, and Percy's power over water to defeat a powerful dark force.