She could be a creation of a powerful witch who has a vendetta against the demigods. The witch uses dark magic to create the succubus and sends her to the Percy Jackson world. The succubus then uses her charm and powers to get close to Percy, either to steal his powers or to use him to get to the other demigods at Camp Half - Blood.
Blue food could be used as a form of currency in the underwater parts of the Percy Jackson universe. For example, blue sea - grapes could be like gold coins for the mer - people. Percy has to learn about this new form of currency when he dives deep into the ocean on a mission.
A succubus can be incorporated as a trainer. She could use her charm and allure to her advantage during battles, perhaps distracting opponents. For example, she might have a unique battle style that involves a bit of seduction.
A succubus familiar can be incorporated by first establishing its magical nature. For example, it could have powers related to charm and allure, which are common traits of succubi. In a fanfiction, it might be a familiar that a dark wizard or an outcast wizard has. The succubus familiar could use its charm to help its master in various ways, like getting information from other characters or sneaking into restricted areas.
In many fanfics, Lucifer's presence can create moral dilemmas for the characters. Percy, who is used to a world of somewhat clear - cut good and evil (in terms of Greek mythology), now has to deal with Lucifer's more nuanced nature. This can lead to interesting internal struggles for Percy as he decides whether to trust or oppose Lucifer.
You could make the succubus drain be part of a curse that was placed on Hogwarts long ago. Maybe it was put there by a dark wizard who wanted to weaken the school's magic. In the fanfic, the characters start noticing that students are getting weaker and tired all the time. They then discover the source is a succubus draining their energy, and they have to search through old books and magic spells to find a way to break the curse.
In some Percy Jackson fanfictions, Excalibur might be incorporated as a powerful weapon that finds its way into the hands of a demigod. It could be a plot device to add more power and mystery to the story.
The morale among the demigods would be greatly affected. The Hunt is often seen as a symbol of strength and unity for female demigods. If Percy kills them, it might create a divide between male and female demigods, leading to internal conflicts within the demigod community. Also, it would change the way demigods view Percy. Some might see him as a hero for eliminating a potential threat, while others would see him as a murderer for killing the Hunt.
The theme of social class in 'The Outsiders' can be used. In 'Percy Jackson' fanfiction, you could create different groups of demigods based on their parentage or abilities. There could be an 'outsider' group of demigods who are looked down upon, similar to how the Greasers were. Percy could then work to bridge the gap between these groups, just as he tries to unite different camps in the original series.
One way is to use the Percy Jackson characters' powers in an Abrahamic setting. For example, Percy's ability to control water could be seen as a gift from God in an Abrahamic fanfiction. Another way is to have the Percy Jackson characters interact with Abrahamic figures. Like Percy meeting an angel and having a conversation about the nature of the world.
Well, perhaps the succubus is sent by an enemy of the gods to disrupt Percy's relationships with his friends. She starts causing jealousy and strife among them by using her alluring powers. Or maybe she's tied to an ancient prophecy that Percy is involved in, and he has to either defeat her or convert her to the side of good to fulfill the prophecy.