In this fanfiction, Harry's life at Hogwarts would be full of new discoveries. He could find secret passages that are overgrown with plants but are only visible to him because of his connection to Demeter. His friends might be a bit in awe of his new powers. He'd also have to deal with some jealousy from other students who don't have such unique abilities. And when it comes to Quidditch, he could use his nature powers to his advantage, like creating a gentle breeze to help him fly faster or making the grass on the pitch grow in a way that confounds his opponents.
He'd probably have a hard time fitting in his dormitory. I mean, he might be too big for the bed! Also, Quidditch would be a whole new ball game. He could accidentally destroy the brooms or the goalposts with his strength. And the other students would likely be either in awe or terrified of him.
Well, it would change a great deal. For one, he might get better grades in Potions as Snape would be more likely to give him extra help. Also, he might be more protected from the likes of Draco Malfoy and his gang, since Snape would not tolerate any bullying towards his adopted son. Harry could also have access to Snape's private library, which would expand his knowledge of magic far beyond what he could learn in the regular Hogwarts curriculum.
In terms of his classes, Defense Against the Dark Arts would be a whole new experience. He could use his Saiyan powers to counter dark magic in ways that no one has ever seen before. He might even develop his own unique spells that are a blend of magic and Saiyan energy, making him a truly formidable wizard - Saiyan hybrid at Hogwarts.
Godric Gryffindor's view might not change much. He'd still see Hogwarts as a place to foster courage, but he might gain new insights from the fanfiction about how students in modern - day interpretations uphold that value. Salazar Slytherin could become more cynical. If he saw his house being misrepresented in some fanfictions as all - evil, he might think Hogwarts has strayed from his original intentions. Helga Hufflepuff would probably feel more positive. The fanfiction that emphasizes kindness and hard work would make her believe Hogwarts is still a great place for nurturing good values. Rowena Ravenclaw might be more open - minded. She'd see different perspectives on Hogwarts in the fanfiction and might consider new ways of teaching and learning in her view of the school.
The story would be drastically different. Without Harry, there's no Boy - Who - Lived to be the main antagonist to Voldemort. Hogwarts might not be the safe haven it was in the original series. Voldemort could target the school more directly, and the students would live in constant fear.
He'd probably be more morally ambiguous. Growing up as Crowley's son, he might not have the same clear - cut sense of right and wrong as the original Harry. He could be more cunning and less hesitant to use underhanded tactics if necessary.
His physical abilities would change drastically. He'd be much stronger and faster. No more getting winded while playing Quidditch. He could probably just fly around the pitch without a broom. And in duels, he could use his Saiyan strength to overpower opponents more easily.
His life at Hogwarts would be very different. He could fly around the castle freely in his phoenix form, which would be quite a novelty. He might use his form to play pranks on the Slytherins in a way that they couldn't easily catch him. Also, his classes would take on a new meaning. For example, in Transfiguration, he could study his own form more closely and learn new things about Animagus transformation. And he would probably be the center of attention among the students, with everyone wanting to see his phoenix form up close.
His relationship with Hermione and Ron would be different. They might be a bit in awe of his new powers. Hermione would be eager to learn more about the Greek god aspects and how it relates to magic, while Ron might be a bit jealous at first but then realize they are all on the same team. His relationship with Dumbledore would also change as Dumbledore would have to guide him in a new way, considering his dual heritage.
His living conditions would change drastically. Instead of living in the wizarding world, he'd be in palaces. He'd have servants and all the luxuries that come with royalty. His friends at Hogwarts would be replaced by new acquaintances in the royal circle. He'd have to adapt to a very different set of rules and expectations.