Perhaps Medusa has some crucial information that Percy needs to save the world, and in order to get that information, he has to protect her from other threats. So he embarks on a journey to keep her safe.
Another way is to check out some Percy Jackson - related fan communities on social media platforms like Reddit. There are often threads where fans share their favorite fanfictions, and you might stumble upon some good 'Percy saves Medusa' ones there.
I don't know for sure as I haven't read this particular fanfiction, but usually in fanfiction, Percy could be a character from a popular book, movie or TV series.
You can develop Medusa by exploring her backstory more. Maybe show how she was before she was cursed, her hopes and dreams. For example, she could have been a beautiful and kind - hearted maiden once. Also, give her some complex emotions like regret for the people she has turned to stone.
One great Percy, Servant, Medusa fanfiction could be one where Percy has to face Medusa in a new context while having a servant. It might explore their mythological aspects in a modern or alternate universe setting. For example, the story could revolve around Percy using his skills and the help of the servant to outwit Medusa, who has some new powers or motives.
It could be a demigod who has been corrupted by the power of Medusa's severed head. He uses the petrifying power for his own evil gains, like trying to turn all the other demigods into stone so he can rule the demigod world alone.
One way to develop Percy is through his interactions with other characters. He could have confrontations with demigods who are suspicious of him. These interactions can force him to defend his existence and his right to be at Camp Half - Blood. At the same time, he could also have positive interactions with those who are more open - minded. This will show his ability to handle different types of relationships and grow as a character.
It really depends on the author. Some fanfictions in this genre can be extremely well - written, with great character development, engaging plotlines, and excellent writing style. However, others might not be as good. You won't know until you actually read it.
I'm not sure specifically as it could be one of many fan - made stories. It might be a story where Nico, a character, does something to save Percy in the context of fanfiction. Fanfiction often takes existing characters and creates new, unique scenarios for them.
I'm not sure specifically as there could be many different interpretations in different fanfictions. But generally, it might involve Luke taking actions to rescue Percy from some sort of danger, like a monster attack or a dangerous situation in the world of their story.