First of all, the entire backstory of Harry's family would be different. In the original, he has the loving memory of his parents, James and Lily Potter. If he was Azazel's son, that family connection would be erased. His place at Hogwarts might also be affected. His relationships with his friends, like Ron and Hermione, would likely be different as well. They might view him with suspicion or his new origin could create a rift. His relationship with Dumbledore would also need to be re - thought, as Dumbledore's guidance was based on Harry's original heritage. Overall, it would be a radical departure from the original story.
Well, for one, his status as the son of two founders would give him a different standing in the wizarding world. He might be more respected or feared right from the start.
Well, in terms of relationships, Harry's friendship with Neville could be strengthened. Neville, who always felt a bit in the shadow of Harry, might find that Harry's new identity as the son of Bastet makes him more relatable. Because now Harry is also dealing with something very different from the normal wizarding heritage. With Snape, Snape might be even more hostile at first as he doesn't understand this new element in Harry, but later could come to respect it. And Harry's relationship with Ginny would be different too. Ginny might be in awe of Harry's new powers and their relationship could develop in a more magical and complex way.
In the 'Harry Potter Son of Azazel' fanfiction, perhaps the plot revolves around a prophecy related to Harry being the son of Azazel. This could lead to a whole new adventure where he has to find out more about his heritage. There might be battles against dark forces that are interested in using Harry's connection to Azazel for their own evil purposes. And Harry would have to figure out how to use this new knowledge to his advantage without succumbing to the dark side.
Harry Potter's personality would be drastically altered. Growing up with Azazel, he would lack the warm and nurturing environment that shaped the original Harry's kind - hearted nature. He might be more aloof and detached from others. Instead of being the hero who stands up for the weak, he could be more interested in using his power for his own gain. His sense of right and wrong would be blurred, influenced by Azazel's amoral ways, and he may not hesitate to use dark means to achieve his ends.
A lot. For starters, Harry's family tree would be completely different. His relationship with Dumbledore might also change as Dumbledore's actions were often based on Harry's connection to his parents. Also, the whole idea of the prophecy would need to be re - evaluated as the supposed 'enemy' is now his father. It would turn the concept of the 'chosen one' on its head.
I'm not aware of any official 'Harry Potter is Azazel's son' fanfic. The Harry Potter series has a very established canon, and such a premise goes against the original lore. It might be a very rare or non - mainstream fan - created idea that doesn't have wide - spread recognition.
His relationships with the other characters are also altered. Dumbledore, for example, had a big role in Harry's life in the original story. But if Harry is Grindelwald's son, Dumbledore's attitude towards him might be more complex. Dumbledore had a history with Grindelwald, and this new connection could make Dumbledore both more protective and more wary of Harry. The same goes for other characters like Snape. Their interactions with Harry would be colored by this new family connection.
The story would also shift in terms of Harry's place at Hogwarts. His sorting into Gryffindor might be more complex. Since he's related to the Black family, which has a history of being in Slytherin, there could be an internal struggle within Harry about his house loyalty. And his friends, like Ron and Hermione, might react differently to this new revelation about his parentage as they've always known him as a Potter.
He'd probably be more confident. Dante is a very confident character, and if Harry is his son, he might inherit that trait. He'd be less likely to be intimidated by bullies like Draco or even the Death Eaters.
Well, it's hard to say exactly. If Harry Potter was raised by Azazel, his entire world view would be warped. Azazel is not a benevolent figure. Harry might grow up to be a much more conflicted character. He could be caught between the dark influence of Azazel and the latent goodness within him. His relationships at Hogwarts would also be very different. His friends might be initially wary of him, and he might have to struggle to prove that he's not a threat.