There's also 'The Lost Friendship'. This one focuses more on a time when there is a rift between Percy, Annabeth and Grover. It shows their individual growth as they try to mend their broken friendship. It's a more emotional take on their relationship and shows that even in tough times, their bond is unbreakable.
Archive of Our Own (AO3) also has a wide selection. The advantage of AO3 is that it has a more organized tagging system. So if you want to find a particular type of fanfiction, like one that focuses on their adventures in a specific location, you can easily find it through the tags.
No, it is not appropriate. Fanfiction involving sexual content about characters from a work, especially if they are underage in the original work (which may be the case in some scenarios related to Grover and Annabeth), is unethical and goes against the respect for the source material and its intended audience.
One appropriate topic could be their adventures together. For example, they could go on a quest to find a lost magical artifact that is crucial for their world. This would focus on their teamwork and friendship.
Annabeth is a great choice. Her intelligence and strategic thinking could add a lot to the story. For example, when Percy and Grover are in a tight spot, she could come up with a clever plan to get them out. Another good character is Tyson. His strength and loyalty would be useful in battles and dangerous situations.
Friendship is a very common theme. Since Percy and Grover are such good friends in the original series, fanfictions often explore their bond further. Another common theme is adventure. They go on various quests in the original books, and fanfictions continue this trend. Also, loyalty, as they are always loyal to each other no matter what challenges they face.
One common theme is loyalty. They are loyal to each other through thick and thin in the stories. Another theme is growth. As they face different challenges in the fanfiction, they grow as characters, both individually and in their relationship. Also, the theme of discovery is often there. They discover new things about themselves, each other, and the world around them.
In a large number of Percy and Annabeth fanfictions, they are indeed presented as soulmates. Their shared adventures, the way they understand each other without many words, and the deep loyalty they have for one another all contribute to this perception. Fanfiction authors often build on their existing relationship from the original works and enhance it to the level of soulmates. They might show it through things like Percy being able to sense Annabeth's distress from afar, or Annabeth always knowing exactly what Percy needs in difficult situations. This soulmate - like relationship makes for very engaging and heart - warming stories in the fanfiction realm.
It could be that Annabeth has a misunderstanding about Percy. She might think he's a threat to her position or status at the camp, so she bullies him to try and keep him in check.