She would change in many ways. Firstly, her appearance might start to show some divine features. Emotionally, she could become more stoic as she tries to live up to the reputation of being Apollo's daughter. Her fighting style might incorporate more light - based attacks and she could develop the ability to foresee events, like having a form of prophecy. This would make her a very different Naruto from the original, as she would be dealing with both ninja and divine powers.
Naruto would likely become more confident. Knowing she is the daughter of a powerful god like Apollo would give her a sense of self - worth. She might also become more in tune with arts like music and poetry, which are associated with Apollo.
His view of the world would expand greatly. If Naruto is a Xenophage in this fanfic, he would be exposed to different types of entities and powers that are not native to his world. This would make him more open - minded and curious. He would start to question the nature of his own world and the existence of other dimensions. His character would develop from a simple - minded, if brave, ninja to a more complex and philosophical figure, constantly seeking to understand the greater mysteries of the universe while still maintaining his core values of protecting his friends and village.
If Naruto were the son of Apollo in a fanfiction, it would transform the story. For one, Naruto's appearance might change to have more of an otherworldly or godly look. His training would not be just about learning ninja skills but also about mastering his divine heritage. The village's perception of him would also shift. Instead of being an outcast because of the Nine - Tails, he might be feared or revered because of his connection to Apollo. His enemies would also be more cautious, knowing he has godly powers at his disposal.
I'm not sure if there is such a specific fanfic. It seems like a very creative and unusual concept. Naruto is from the Naruto universe which has its own set of lore and characters, and Apollo is from Greek mythology. Combining them in such a way would be quite a departure from the original Naruto story.
Naruto's character could develop a sense of pride that he didn't have before. This Super Saiyan 3 form is something extraordinary, and he might start to show it off a bit. But at the same time, he would also have to learn humility. If he becomes too arrogant, his friends might distance themselves from him. So he would be in a constant struggle between showing off his power and being the humble ninja he was raised to be. Also, his leadership skills might improve as he now has a power that others look up to, and he would need to lead by example when it comes to using this power responsibly.
It would make him more versatile. He's known for his Rasengan, but using the Chidori would show that he can adapt other powerful techniques. This could make him seem more of a prodigy, as the Chidori is a difficult technique.
His view on power could shift. Instead of relying solely on his own chakra and the Nine - Tails' power, he may start to consider other ways of obtaining and using power, similar to how Cell absorbs power from others. This could make him more open - minded about different forms of strength in the ninja world. He might also become more interested in biological or cellular - level forms of power manipulation, which is a big part of what makes Cell so powerful.
Naruto would likely be more cunning. Since Orochimaru is known for his devious ways, Naruto might inherit some of that. He could be more calculating in battles rather than just relying on brute force. However, he would still have his core of kindness. So, it would be an interesting mix of Orochimaru's slyness and Naruto's big - heartedness.
It could make Naruto more cautious. Since the Ichibi is a powerful and somewhat unpredictable force, Naruto would need to be more careful in his actions. He might think twice before jumping into a fight, as he has to consider the well - being of the Ichibi as well.
Naruto's morality could be somewhat skewed. Orochimaru has a very different view on right and wrong compared to Naruto. So, Naruto might start to question some of his previous beliefs. For example, he might be more willing to use dangerous or forbidden jutsus if it means achieving his goals. He'd also probably be more distrustful of others, as Orochimaru always has ulterior motives. This would be a big change from the Naruto who was always so quick to trust and befriend people.
Naruto would become more brooding. His usual cheerful self would be dampened by the dark nature of being a vampire slave. He'd be more secretive as he has to hide his new condition from his friends at first.