Perhaps the daughter inherits some unique magical abilities from both her parents. Harry's ability to face Voldemort fearlessly and Draco's cunning and resourcefulness could combine in her. She might use these skills to solve mysteries around Hogwarts. Like, there could be an ancient magical artifact that has been lost for centuries and she, with her combined traits, is the only one who can find it. And in the process, she discovers more about the history of Hogwarts and how her parents' pasts are intertwined with it.
Well, she could be highly intelligent like Hermione. Maybe she'd be a bookworm, always with her nose in a tome, eager to learn new spells and knowledge. At the same time, she might inherit Draco's sense of pride. So she'd be confident in her abilities and not easily intimidated. However, she could also have a kind heart, a blend of Hermione's compassion and Draco's loyalty to his own, which in this case would be his family.
She could be highly intelligent like both her parents. Since Hermione is known for her studiousness and Draco is quite cunning in his own way, their daughter might inherit a sharp mind. She could be very confident, perhaps a bit of a loner at times as she might feel she doesn't quite fit into the typical Hogwarts houses' stereotypes. And she might have a strong sense of justice, but also a bit of a mischievous streak from Draco.
If Harry is Salazar, he might have enhanced Parseltongue abilities. Salazar was known for his connection with snakes, so Harry could communicate with a wider variety of serpents and perhaps even gain more control over them. For Draco as Godric, he could have a stronger affinity for Gryffindor - like magic, such as a more powerful Patronus, perhaps in the form of a lion, representing Godric's courage.
The family house - elf could be an important character. It could be the one who takes care of the family home and the kids when Harry and Draco are away on magical business. It could also be a confidant for the children, listening to their problems. And Dumbledore's ghost could make an appearance. He could offer some cryptic advice to Harry and Draco about raising their family in the wizarding world, guiding them to make the right decisions for their family's future.
Draco would probably be very protective. Given his own experiences at Hogwarts and in the wizarding world, he wouldn't want Lyra to get into any dangerous situations. He might be strict in teaching her about the pure - blood values that he grew up with, but also show a soft side when it comes to her personal interests and dreams.
Yes, there are quite a few fanfictions with the concept of Harry and Draco being mates. In the world of fanfiction, writers often explore different relationship dynamics between characters that deviate from the original canon. This can lead to some really interesting stories where Harry and Draco form an unexpected bond, whether it's a friendship, a more complex relationship, or a new kind of magical connection.
One possible plot could be that Harry and Draco, after years of rivalry and then gradually getting to know each other better, find themselves in an unexpected situation where they have a child together. Maybe it starts with a magical accident that binds their magic in a way that results in a baby. They then have to deal with the shock from their friends and family. Harry's friends like Ron might be initially very skeptical and angry, thinking Draco is up to something. But as time goes on, they see that Draco has changed and that he and Harry truly care for the baby and each other.
Maybe Harry has seen a different side of Draco that others haven't. He could have realized that Draco was just a product of his upbringing and the difficult situation he was in.
Maybe in some fanfictions, Draco is driven by a sense of self - preservation. He might believe that Harry will eventually turn against him or the Slytherin house. He could think that by killing Harry, he can secure his own place at Hogwarts and in the wizarding community. Additionally, it could be part of a larger plot by Voldemort or his followers. If Draco is forced to join Voldemort's side, he may be given the task of killing Harry to prove his loyalty.