Percy is likely a character within the context of this fanfic. Without more information, it's hard to say exactly who he is, but he's probably someone with the ability to take the power of things he kills.
No, it's not appropriate. Fanfiction should generally uphold moral and ethical standards. Writing about such intimate and private aspects in a sexual context is disrespectful to the characters and can make many readers uncomfortable.
One common theme is family. Paul steps in as a father - figure to Percy, showing that family doesn't always have to be blood - related. Another theme is growth. Percy grows and matures under Paul's care.
I don't think there should be such fanfiction as it goes against the established lore and ethics in the original context. In most mythologies, Hera is a major goddess with a certain status, and creating such inappropriate content is disrespectful to the source material.
There is a story titled 'Paul's Support for Percy' which is a great piece of this kind of fanfiction. In it, Paul is portrayed as a very understanding figure. He takes care of Percy by being there for him when Percy is facing challenges at school and in his demigod life. He cooks for Percy, listens to his problems, and gives him advice, which really helps Percy grow and become more confident.
In fanfiction, if Percy Jackson takes over Olympus, he might bring a new order. He could reform the archaic rules of the gods. For example, he might ensure fairer treatment of demigods, like better training and protection. Also, he could change the power dynamics among the gods, making them more accountable for their actions.
One heartwarming moment could be when Percy makes Annabeth her favorite soup from scratch. He carefully follows the recipe, even though he's not the best cook, just to make her feel better.
Well, it could be that in this fanfic, Percy has the unique ability to absorb the powers of the beings he kills. This might make him extremely powerful as he accumulates various abilities over time.
His friends from Camp Half - Blood would likely support him. Annabeth, with her strategic mind, would be a great asset. Grover, too, would stand by Percy. Also, the younger demigods who have seen Percy's heroic deeds would probably back him as they look up to him.
One possible scenario could be that Percy got injured and Annabeth needs to tend to his wounds on his torso, so she takes his shirt off. For example, he might have been scratched by a monster during a battle, and she has to clean and bandage the wound quickly.