The way Harry deals with his enemies would be different. Captain Marvel is very direct in combat. Harry, under her influence, might be more aggressive in facing Voldemort and his Death Eaters. Instead of waiting for Voldemort to make the first move in some cases, he could be more proactive in seeking out and confronting the dark forces. Also, his relationships with other characters could change. His friendship with Ron and Hermione might have a different dynamic as he grows up with Captain Marvel's values.
His attitude towards authority might change. Captain Marvel often challenges authority when it's unjust. So Harry might be more likely to question the Ministry of Magic's decisions. For example, he might not be as hesitant to oppose Umbridge in Hogwarts.
Harry would be exposed to a lot more advanced technology. Captain Marvel has access to advanced Kree technology. This could influence how Harry views magic and technology. He might try to find ways to combine them, like creating magical devices with the help of Kree tech principles. This would make his adventures not only about magic but also about this unique blend of magic and technology.
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.
The story would be unrecognizable. His character would be different, and so would his relationships.
He'd be more adaptable. Quarians live in a different way than wizards, so Harry would learn to be flexible in new situations.
He would likely be more confident in his physical abilities. Yoruichi is a very capable fighter, and if she raised Harry, he would be trained in combat. So he might not be as hesitant in dangerous situations as the original Harry. He could be more likely to take risks and trust in his own strength.
His story would be drastically different. He might not have the same fear of Voldemort as he would be in a different environment. Instead, he could be facing threats related to Rias' world like other devil clans or powerful supernatural beings.
His view of family would be different. Vikings had a strong sense of clan. So instead of longing for a family like he did in the original story, he'd be part of a large Viking family unit. His magical abilities might be more of a mystery to the Vikings around him, and they could either fear or revere him for it.
He would be more cunning. Maleficent is a master of manipulation, and Harry would likely pick up on those skills. He might be less naive compared to the original Harry.
He'd be more reserved. Vergil isn't exactly a talkative and outgoing person. Harry would likely follow suit, keeping his thoughts and feelings to himself more often.
Harry would probably be more attuned to dark magic. His upbringing by Satan would expose him to different forms of magic and he would have a different understanding of power. He might be more ruthless in achieving his goals and less concerned about the consequences for others. For example, in the original series, Harry was always worried about the safety of his friends, but in this fanfiction, he might use his friends as pawns if it served his purpose.