Harry would likely develop a very different personality. He may be more solemn and less prone to the typical teenage angst that the original Harry had. Since he is raised by Death, he might be more in tune with the darker aspects of life and magic from a young age.
One great 'Fem Harry Potter Raised by Death' fanfiction is 'The Girl Who Lived'. It offers a really interesting take on how a female Harry Potter's personality would develop under Death's guidance. The story has some unique magical elements and a great plot that keeps you hooked.
Dumbledore would still be an important character. His interactions with Harry, who is raised by Lady Death, would be filled with a lot of mystery and caution. He might try to understand the implications of Harry's upbringing and how it affects the balance of power in the wizarding world. Hermione and Ron could also be main characters. Their friendship with Harry might be strained at first as they try to understand his new and rather dark - influenced personality, but they would still be important in Harry's life as they support him in different ways and help him navigate the challenges he faces at Hogwarts.
One possible plotline could be that Harry gains unique powers or a different perspective on magic due to being raised by Lady Death. For example, he might have an uncanny ability to understand and manipulate the darker aspects of magic in a way that others can't.
Well, in such fanfiction, a common plotline is Harry being trained in secret Death Eater techniques. This would make him a formidable wizard in a different way than in the original books. He could also be used as a pawn by the Death Eaters against Dumbledore and the Order of the Phoenix, leading to some intense battles and strategic moves. And his connection to Voldemort might be even more muddled, as the Death Eaters may try to manipulate that for their own gain.
Well, perhaps his relationships with other characters would be drastically different. He might be more of an enigma to his friends like Ron and Hermione. Instead of growing up in the wizarding world with its normal social norms, he could have a more detached and otherworldly view. This would lead to some really interesting interactions, like when he first enters Hogwarts and the teachers don't quite know how to handle him.
One common theme is power. Since she's raised by Death, often Fem Harry has a different kind of power or a deeper understanding of magic. Another theme is identity. She has to figure out who she is in a world that expects a male Harry Potter. For example, in some fanfictions, she struggles with how to fit into the role of the 'Chosen One' when she's a girl.
One possible plotline could be that Harry has unique magical abilities due to being raised by Death. Maybe he can communicate with the dead more easily and gain knowledge from them that gives him an edge in the wizarding world.
Voldemort would remain a major character. Harry's new abilities and perspective from being raised by Death would make their conflict even more complex. Harry might approach the fight against Voldemort with a different strategy, one that is influenced by the teachings of Death.