Perhaps Harry is teaching Potions in the fanfiction. Since he had a bit of a rocky start with Potions in his student days, he could be a very understanding teacher. He might encourage students to experiment more, which is different from Snape's strict methods. He could also share stories about how important Potions were in his adventures, like when they made Polyjuice Potion. This would make the class more interesting and inspire students to take Potions more seriously.
Hermione would surely be a main character. She could be a fellow teacher, perhaps teaching Transfiguration or History of Magic. She would be the one Harry goes to for advice on teaching methods or when he has a difficult student. Another character could be Ron. He might visit Harry at Hogwarts and end up getting involved in some of the school's mysteries or helping Harry with a particularly difficult Quidditch - loving student.
Perhaps the story could revolve around them facing challenges within the Hogwarts faculty. There could be some old - fashioned professors who oppose their modern teaching methods. Harry and Hermione then have to prove that their ways are beneficial for the students. They might also discover new magical abilities in some of the students that were previously overlooked, and help those students develop their skills.
Well, perhaps Harry Dresden could introduce his unique brand of magic from his own world into Hogwarts. He might teach the students new ways of dealing with magical creatures that are different from the traditional Hogwarts methods.
I think younger readers who are fans of the Harry Potter series and are looking for something a bit different would be interested. They might be intrigued by the idea of a new character, Harry Dresden, coming in and shaking things up at Hogwarts. And for those who like to explore different interpretations of magical worlds, this fanfiction would be right up their alley.
Snape could also be the one to teach Harry a lesson. Given their complex relationship in the original books, in fanfiction, Snape might see an opportunity to put Harry in his place. For instance, if Harry fails in a potions class because of his carelessness, Snape could use this as a chance to teach him about discipline and attention to detail.
In the fanfiction world, Harry might be the heir to Hogwarts if there was some sort of magical pact made generations ago. For example, perhaps one of his ancestors had a special role in the creation or protection of Hogwarts, and this role was passed down through the family. It could also be that his unique magical abilities, like his ability to resist Voldemort's attacks from a young age, are signs of a deeper connection to Hogwarts itself. This connection could be what designates him as the heir in the fanfiction's plot.
One spell she could teach is a charm for protecting books from any kind of damage. Given Hermione's love for books, this would be a great addition to the curriculum. Also, a spell for magically highlighting important parts of textbooks as you read them would be very useful. This spell could be activated by just thinking about the relevant information while reading.
Maybe Harry would teach Tom about the consequences of dark magic. Since Harry has faced Voldemort multiple times and seen the destruction caused by dark spells. He could use these real - life (well, in the wizarding world) examples to make Tom understand that there are other paths in magic that are more positive and life - affirming.
One possible reason could be that he was under the influence of a powerful dark magic or a curse that made him lose control. Another reason might be that he was tricked into believing Hogwarts was a threat to the wizarding world in some extreme way. Maybe a powerful enemy manipulated him to think that destroying Hogwarts was the only way to save everyone.