Harry would be a more confident and brave individual. Captain America's influence would make him less afraid of challenges. In the wizarding world, he would approach his studies and the fight against dark magic with more determination. He would also be more respectful of authority, but not blindly so. If he saw something wrong with the wizarding authorities, he would try to change it in a more diplomatic way, learned from Steve's leadership.
It could be really interesting. Maybe Harry would grow up with a different kind of magic education system in America. He might attend Ilvermorny instead of Hogwarts. His friends could be American witches and wizards with different cultural backgrounds and accents.
The story would be completely different. Harry would probably have a very different personality. Instead of the somewhat shy and uncertain Harry we know, he could be more confident and assertive like Captain America. His magical abilities might be used in a more strategic way, similar to how Steve uses his combat skills. And the wizarding world would have to deal with a Harry who has a very different upbringing and set of beliefs.
Well, first of all, Harry would probably have a more intergalactic view of the world. Captain Marvel has experience with different planets and species. This could make Harry more aware of the bigger universe outside of Hogwarts. Also, his magical abilities might be combined with some of Captain Marvel's combat training. He could be a more physically formidable wizard, using his magic in more combat - oriented ways like Captain Marvel uses her powers.
Well, in a 'Harry Potter raised in America' fanfic, the cultural differences would play a huge role. For example, the magical community in America might be more open to new forms of magic or technology. Harry could be involved in things like American wizarding sports which are different from Quidditch. Also, the way magic is taught in American schools could be more hands - on or practical - oriented.
If Harry Potter was raised in Storybrooke, it would be really interesting. He'd probably grow up with a different set of values. In Storybrooke, the concept of good and evil is often more complex and intertwined. Harry might be more used to dealing with morally grey areas compared to the more clear - cut division in the wizarding world. Also, he might find new ways to use his magic, perhaps influenced by the fairy - tale - like magic in Storybrooke.
Well, if Harry Potter was raised by the God of Life, he would probably be a very different person. For one thing, his upbringing would likely be filled with teachings about the cycle of life and death. This could make him more empathetic towards those who have suffered losses. Also, his magic might be more attuned to life - giving spells and he could potentially bring new life to areas that have been damaged. Maybe he would be less vengeful towards Voldemort and more focused on redeeming him through the power of life.
Well, if Harry Potter was raised by the Joker, he would probably be trained in a very different set of skills. Instead of learning magic in a traditional Hogwarts way, he could be taught how to be a master of chaos and trickery. His values would be completely different too. He might not have the same sense of justice and good that he has in the original story. The Joker's influence could lead Harry to question the very concept of right and wrong. And his relationships would be strange. He may not form the same kind of friendships as he did in the wizarding world. He might be more isolated or form alliances with those on the darker side of the magical or Muggle world.
His life would be a blend of the magical world of Harry Potter and the ninja world elements from Kushina. He might grow up with a strong sense of family, as Kushina was very family - oriented. He could also inherit some of her ninja skills, making him a unique wizard with both magic and physical combat abilities.
His life would be full of magic in a very different sense. Alduin, being a powerful dragon from the Elder Scrolls universe, would teach Harry about a different kind of power. Harry might grow up learning to control dragon - like abilities. He could be more in tune with nature and primal forces rather than the traditional magic he learned at Hogwarts.
In fanfiction, Harry Potter's training in America might involve learning different magical techniques. He could be introduced to Native American magic which has its own unique elements. Maybe he'd study in a hidden American wizarding school where they focus more on practical magic for modern-day situations.