The relationship might turn into one where Harry has to constantly remind Dumbledore of who he is and their shared experiences. Dumbledore, in his senile state, could forget important things about Harry like his role in the fight against Voldemort. Harry would then have to patiently re - introduce himself and the situation. This could be frustrating for Harry at times, but it could also deepen his understanding of Dumbledore as a more human and fallible figure.
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.
Well, in certain Harry Potter fanfiction, Dumbledore can come across as insane. It really depends on the writer's interpretation and the direction they want to take the story. Some might do it for shock value, to create a more edgy or different take on the well - known character. However, the canonical Dumbledore was a highly intelligent and calculating figure, not insane.
Well, Harry might outsmart Dumbledore by using his unique understanding of the magical world in ways Dumbledore doesn't expect. For example, Harry has a more direct experience with some dark magic items due to his encounters with Voldemort. He could use this knowledge to make decisions that seem counter - intuitive to Dumbledore but are actually more effective in a particular situation.
He might give Harry detention. Harry could be made to clean the trophies in the trophy room or help Hagrid with some difficult tasks in the Forbidden Forest under strict supervision.
One possible reason could be that Harry breaks school rules in the fanfiction. For example, if he ventures into the Forbidden Forest without permission. Dumbledore is strict about the safety of students and such disobedience might lead to punishment.
In a fanfiction, Dumbledore might steal out of desperation. Suppose there was a situation where a curse was about to be unleashed on Hogwarts, and the only way to stop it was by stealing a particular ingredient for an antidote from a place where it was not supposed to be taken. Dumbledore, seeing no other option, decides to steal it. His motive here is to save the school and its students, even if it means breaking the rules.
Hermione could be a main character. She might use her vast knowledge to help Harry and Dumbledore in their adventures. For example, she could research ancient spells or potions that are crucial for their mission.
For Harry, his friends like Ron and Hermione are likely to be his allies. They've always been by his side through thick and thin in the original series, so it's natural for them to support Harry in a confrontation with Dumbledore. Neville could also be an ally, given his growth and courage shown in the books.
In my opinion, Dumbledore would underestimate Harry Potter fanfiction. Fanfiction is a realm where fans take the original story and run with it in all kinds of directions. There are fanfictions that change the personalities of characters, create new storylines that deviate greatly from the original. Dumbledore, who is bound by the original narrative and his role in it, may not understand the significance of this new wave of creativity that fanfiction represents. He may see it as a distortion of the world he knows rather than a celebration and expansion of it.