A possible plot idea is that the duel is a miscommunication. Dumbledore thinks Harry has been influenced by dark magic, and Harry thinks Dumbledore has turned against him. As they duel, they gradually realize the misunderstanding and work together to find the real source of the problem. Or perhaps it's a time - traveling duel where future - Harry has to duel past - Dumbledore to prevent a dark future.
One interesting fanfic could be where Harry has to duel Dumbledore in an alternate reality where dark magic has corrupted the school. In this story, Harry discovers new spells to use against Dumbledore's powerful magic. Another might involve a time - travel plot where a future student duels Dumbledore to prevent a great disaster. There could also be a fanfic where a new character, who has unique magical abilities, challenges Dumbledore to a duel to prove their worth.
One idea could be Dumbledore misplacing his memories and the students of Hogwarts having to help him retrieve them. It could lead to a series of adventures where they discover secrets about Dumbledore's past that were long forgotten.
A really interesting plot could be that Ariana's spirit is trapped in a limbo of sorts. Harry, with his penchant for getting into extraordinary situations, discovers a way to communicate with her. They then work together to free her spirit. Along the way, Harry learns more about Dumbledore's past through Ariana's memories, which in turn helps him in his own battles against the remaining dark forces in the wizarding world.
Harry could develop his strategic thinking. In a duel with Dumbledore, he would be forced to think several steps ahead. This would make him more calculating and less impulsive in his actions. Also, his relationship with Dumbledore would change. If he loses the duel gracefully, he might gain a new level of respect for Dumbledore's power and wisdom. On the other hand, if he wins, he might feel a sense of responsibility that comes with being on a more equal footing with the great wizard.
Yes, there is a fanfic where a young Slytherin student duels Dumbledore. Throughout the duel, the Slytherin discovers his own moral compass and realizes that Dumbledore is not the enemy he thought. This duel becomes a turning point for the Slytherin's character growth, as he starts to question the values he was taught in his house.
In such a fanfiction, perhaps a major plot point is how Dumbledore trains Harry to face a new and greater threat. It could be a dark wizard more powerful than Voldemort, and Harry has to learn a whole new set of strategies and magic under Dumbledore's guidance. Harry might also develop a deeper understanding of the wizarding world's history and secrets through Dumbledore's teachings, which could be a key part of the plot.
Well, some fanfictions might focus on Ariana's magic. Since her magic was unstable, a story could revolve around her learning to control it in a different way than what Albus and Aberforth thought was best. This could lead to a split in their family not just because of the incident with the Muggle boys but also due to differences in how to handle Ariana's powers. Or, there could be a time - travel based fanfic where a character from the future tries to save Ariana from her tragic fate, changing the course of the Dumbledore family history.
One plot idea could be that Harry and Angelina team up for a special Quidditch training session for the younger students. They discover a new flying technique together that gives Gryffindor an edge in future matches. Another could be that they go on a secret mission within Hogwarts to uncover a hidden artifact that has been causing strange magical disturbances. And a third idea is that Angelina gets injured during a match and Harry uses some of his unique magical skills, learned from his various adventures, to help her recover faster than normal.
One idea could be a story where a character has a special power to resist Dementors' effects more than others. Maybe they discover a hidden spell or have a unique magical ability that they use to fight off Dementors when others are in danger. For example, a young witch or wizard who can emit a positive energy that counteracts the Dementors' despair.
One idea could be Norberta getting lost in the Forbidden Forest and Harry has to find her. Another could be Norberta growing ill and Harry, with his knowledge of magical creatures, tries to heal her. Maybe Norberta could get into trouble with some other magical creatures and Harry has to step in to protect her.