It could be Professor McGonagall. She is always looking out for Harry and has escorted him on various occasions in the original books. She is strict but fair, and if Harry is in some sort of situation where he needs guidance, she would be a likely candidate.
I'm not entirely sure if there is a specific 'Harry Potter is a teacher' scenario within Twilight fanfiction. Twilight and Harry Potter are two very different universes, and while fanfiction can be quite creative and cross - over in strange ways, this particular combination seems rather unusual.
Another option could be Hagrid. Harry has a very close relationship with Hagrid. As a teacher's assistant, Harry could help Hagrid with his Care of Magical Creatures class. He could assist in taming some of the more difficult creatures, and also help the students feel more at ease around the sometimes - scary magical beasts. Harry's own experiences with magical creatures would make him a great choice to assist Hagrid.
One common theme is mentorship. Harry, as a teacher, often takes on the role of mentoring the young students. He uses his own experiences of growing up, facing Voldemort, to guide them through difficulties.
Maybe Professor McGonagall. She was strict but also had a soft spot for Harry. She might take Harry under her wing more in this fanfiction and make him her 'pet' student. She could teach him advanced Transfiguration skills or involve him in Gryffindor - related leadership tasks that give him an edge over the other students.
Well, the teacher's character could be developed through her relationships with students. For example, if she has a particularly difficult student who challenges her beliefs in divination. This forces her to re - evaluate and grow. Maybe she starts off as a bit of a strict traditionalist, but as she interacts with the student, she becomes more open - minded.
One reason could be for educational purposes. The alley is full of unique magical items and people, so the teacher might want Harry to get some hands - on experience with the real - world applications of magic.
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.
Yes, there are quite a few. For example, some fanfictions focus on a new teacher arriving at Hogwarts and having all sorts of adventures with the students. They might bring in new spells or ways of teaching magic that add an interesting twist to the familiar Harry Potter world.
He would probably be a very inspiring teacher. He has so much real - life experience with magic, from fighting dark wizards to solving mysteries. He could teach Defense Against the Dark Arts in a way that no one else could, sharing his own combat strategies and knowledge of dark creatures. His students would surely be in awe of him and eager to learn from his adventures.