At first, it might be a bit tentative. Harry has to earn Buckbeak's trust, just like in the original story. But as time goes on, they start to understand each other better. Buckbeak realizes Harry is different from other humans who might harm him, and Harry sees Buckbeak as more than just a magical creature.
Well, they might go on a journey to find a hidden magical artifact. Maybe they encounter some dark wizards along the way and have to use Buckbeak's flying skills and Harry's magic to escape.
The main characters are clearly Harry Potter and Buckbeak. Harry is the famous wizard boy from Hogwarts, and Buckbeak is the hippogriff that Harry befriends in the series.
Well, it depends on the specific fanfiction. Some fanfic authors might see the connection between Fawkes and Harry and make Fawkes his familiar. Fawkes is a phoenix with special powers, and having it as a familiar could add an interesting dynamic to Harry's story in the fan - made versions. It could help him in various ways, like providing magical support or even acting as a sort of guide. But not all fanfictions will have this relationship.
There's 'The Adventures of Harry, Hermione and Buckbeak'. It has a really interesting plot where they use Buckbeak to explore ancient wizarding ruins. There are lots of cool details about the ruins and how they interact with the environment around them using magic.
There might be a fanfiction where Buckbeak plays a crucial role in protecting Hogwarts. He could use his sharp eyes and powerful wings to spot incoming threats before the students and teachers are aware. For example, he might notice a group of Death Eaters approaching and warn the school in time. He could also carry important messages between different parts of the school or even outside of Hogwarts to get help when needed.
For Harry, his friends in Gryffindor could be a bit confused at first. They know Draco is not exactly a friendly character. But overall, it could lead to a more united front against real threats in Hogwarts. The teachers might also take notice. Dumbledore, for instance, would probably be proud of Harry for showing such selfless courage, regardless of who he was saving.
One interesting plot could be Buckbeak helping Harry in a secret mission outside Hogwarts. Maybe they have to find a hidden magical artifact that is crucial for the safety of the wizarding world.
Hermione would be a great addition. She could use her vast knowledge of magic and research skills to help Harry and Buckbeak in their adventures. For example, if they were on a quest to find a rare magical herb to cure Buckbeak of a strange illness, Hermione would know exactly where to look.