Her relationship with the camp counselors would be really complex. They have to protect the camp and its inhabitants, so they'd be hesitant to fully trust her. However, as she participates in camp activities and battles, she could earn their respect. In terms of romantic relationships, a son of Athena might be initially attracted to her intelligence but then struggle with her heritage. And she might have a mentor - like relationship with an older demigod who has also had a difficult family history.
Her relationship with Hermes could be really interesting. Since Hermes is the messenger god, he could be the one to help her understand the complex world of the Greek gods. They might start as just acquaintances, but as she needs to send messages or get information quickly, they become closer friends. With Athena, there could be a bit of a rivalry at first because Fem Harry is intelligent and so is Athena. But over time, they could learn from each other and respect each other's wisdom.
His relationship with the gods would be super interesting. The gods would be very wary of him. Zeus, in particular, would probably want to keep an eye on him or even try to eliminate him. But some of the more benevolent gods, like Poseidon (even though he's not Percy's father in this fanfiction), might give him a chance. Percy would have to navigate this tricky political situation among the gods while also trying to find his place in the world.
Her relationship with Percy would be very interesting. Since Percy is a son of Poseidon and she is the daughter of Chaos, they would have different outlooks. Percy is used to the order of the Olympian world to some extent, while she represents chaos. But they could also find common ground in their heroism. She might be a bit of an enigma to him at first, but over time, they could develop a mutual respect. With Annabeth, there could be some initial friction as Annabeth values logic and order, which the daughter of Chaos might seem to disrupt. However, they could learn from each other, with the daughter of Chaos teaching Annabeth to be more flexible and Annabeth teaching her about strategy.
His relationship with Annabeth would be really strained. Annabeth is a firm believer in the gods, and if Percy is the son of Kronos, she would be very suspicious and probably feel betrayed. She might even try to fight Percy at first, thinking he's a threat to her and her friends.
The relationship with Poseidon would be extremely complicated. Poseidon would be torn between his love for Percy and his fear of what Percy could become as Kronos' twin. He might try to distance himself from Percy at first, which would deeply hurt Percy. On the other hand, Percy's relationship with some of the minor gods might improve. Since they are often overlooked by the major gods, they might see Percy as a potential ally in changing the status quo. Percy's relationship with Luke, if he were still alive in this fanfiction, would also be interesting. Luke might try to use Percy's connection to Kronos to his advantage, but Percy would have to be careful not to be manipulated by Luke.
Her relationship with Thor would be complex. He would be her father, but they might have initial misunderstandings due to their different upbringings. Thor might be overprotective at first, which could cause some friction between them. However, as they get to know each other better, they would develop a strong bond.
In terms of her relationship with the gods, the goddesses might take a special interest in her. Athena might view her differently than she did Percy. She could either see her as a threat or as a potential ally in the world of mortals. And Poseidon, as her father, might have a more nurturing relationship with her as a daughter, which could be different from his relationship with the male Percy.
One plot idea could be her struggling to hide her true identity within Camp Half - Blood. Since Kronos is a major villain, the other campers might be hostile if they find out. Another idea is her trying to redeem her father's name in some way, perhaps by finding a way to undo some of the harm he caused. A third could be her having a special power due to her heritage that she has to learn to control while also dealing with the stigma of being Kronos' daughter.
Her relationship with Dumbledore would be extremely complex. Dumbledore, knowing her parentage, would be both watchful and perhaps a bit more guarded around her. He would try to guide her away from the dark path but also might not fully trust her at first. With Ron and Hermione, they might initially be shocked and a bit hesitant. However, their loyalty to her as a friend could eventually overcome their doubts, but there would always be a bit of unease, especially when it comes to using dark magic.
Her relationship with Sasuke could be really different. Since she can't express herself verbally, Sasuke might initially misunderstand her. But as he gets to know her better, he realizes that her actions speak louder. For example, when she saves him from danger, he starts to see her in a new light. With Sakura, they might develop a more sisterly bond as Sakura tries to help Fem Naruto communicate in different ways.