Well, first of all, she'd be highly perceptive. Snape was always observing and analyzing, and his daughter would likely do the same. This would make her a good judge of character. She'd also be determined, just like her father was in his various pursuits. Whether it was in her studies or in helping her friends, she wouldn't give up easily. And in terms of emotions, she might be a bit brooding at times, like Snape. But she could also have moments of great passion, especially when it came to things she truly cared about, such as justice or protecting the innocent, which was something her father ultimately fought for.
She would likely be very intelligent. Snape was a brilliant wizard, and he would surely pass on his knowledge and love for learning. She might also be a bit reserved and guarded, just like her father. His experiences made him cautious, and she could inherit that trait. And she'd probably have a strong sense of loyalty, especially towards those she cares about, as Snape was ultimately loyal to Dumbledore and the cause of good.
Her personality could be greatly influenced by her father. Severus Snape was known for his sarcasm and dry humor, and she might pick up on that. She could use sarcasm as a defense mechanism. Also, his ability to keep secrets would rub off on her. She might be the type to keep her own counsel and not easily trust others with her innermost thoughts. However, she could also have a softer side, perhaps a result of seeing the good in her father that others didn't always notice.
Her personality would likely be strong - willed. Since Artemis is a powerful and independent goddess, Bella would inherit some of that strength. She would be confident in her abilities, especially those related to the outdoors like hunting and survival.
Well, her experience at Hogwarts could be quite different in many ways. Since Harry had faced so many challenges and life - threatening situations during his time at Hogwarts, the school would have tightened security in some ways. So she might find it a bit more restricted in some areas. But at the same time, because of her father's influence, she could have access to some special privileges. For example, she might be allowed to visit the Forbidden Forest more often for research purposes if she shows an interest in magical creatures. Also, her social life would be different. Harry had a rather small group of very close friends, but she could be more of a social butterfly, flitting between different groups in different houses. This would give her a broader perspective on the different cultures within Hogwarts. And in terms of her academic performance, she might be under more pressure to excel not just for herself but also to uphold her father's name. But she could also use her father's knowledge and experiences as a source of inspiration and guidance to do well in her studies.
Snape is a complex and often brooding character. His daughter might initially find it difficult to get close to him. He would probably be strict in teaching her magic, especially potions. But his underlying love and protectiveness would show in small ways, like making sure she has all the ingredients she needs for her potions work. His reserved nature might make her feel like he doesn't care much, but as she grows older, she would understand that his actions speak louder than his words.
As a wolf Animagus, Snape might be more in touch with his primal instincts. His usual guarded and calculating personality could be tempered by the wild nature of the wolf. He may be more impulsive in his actions, acting on instinct rather than over - thinking every move like he does in his human form.
She could be highly competitive. Growing up with the legacies of Naruto and Ino, she'd always strive to be the best. This competitiveness could drive her to train harder and learn new techniques faster. However, it might also cause some friction with her peers at times. But overall, she'd be a well - rounded character with a strong sense of justice and loyalty, influenced by her parents' values.
She could be very determined. If she sets her mind on something, whether it's winning the House Cup for her house or solving a mystery in the Forbidden Forest, she won't give up easily. Her determination could come from Hermione's never - say - die attitude and Draco's single - mindedness when he wants to achieve something.
She might be more empathetic. In the original, Orochimaru is quite cold and calculating. As a girl, she could still be intelligent and ambitious but also show more understanding towards others. For example, she might hesitate more before harming someone if she can sense their good intentions.
It would be extremely complex. Harry might initially be in disbelief and struggle to accept Snape as his father. Snape, on the other hand, would probably be very strict but also deeply protective in his own way.
Yes, there are such fanfictions in the Harry Potter fandom. Some fans like to explore this alternative family relationship through their creative writing.
Snape would probably be initially reluctant. He has always had a somewhat prickly relationship with the Gryffindors, and Hermione is no exception. But his sense of duty as a healer or someone with the knowledge to help would eventually make him step in.