Yes, there are some out there. You can start by looking on fanfiction websites like Archive of Our Own. Some fanfictions might explore the unique relationship between a character from Harry Potter and Charlie from Twilight, perhaps in a crossover adventure where they team up to face a common threat or solve a mystery that spans both their magical worlds.
No. 'Twilight' is an entirely separate and original work with its own unique story, characters, and themes. It has no relation to being a 'Harry Potter' fanfiction.
One common theme is the clash of different magical systems. Since Harry Potter has wand - based magic and Twilight has vampire and werewolf abilities, seeing how they interact is often explored. Another theme is the exploration of new relationships. The fem Harry Potter character gets to form relationships with Twilight characters, which can be both friendly and romantic.
One interesting concept could be a wizard attending Forks High School. Imagine a Hogwarts student having to adapt to the non - magical yet vampire - filled environment of Forks. It would be a clash of two very different magical and supernatural worlds. For example, they might try to use magic subtly without being noticed by the vampires or werewolves.
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.
Some Twilight - Harry Potter fanfiction had a following. There were fans who liked the idea of mashing up the two universes, with elements like vampires and wizards interacting. However, it wasn't as mainstream as pure Harry Potter or Twilight fanfiction on their own.
One common theme could be the clash of different magical systems. Harry Potter has its own set of spells and magic, while Twilight has vampires and werewolves with their own abilities. Another theme might be friendship or alliance building between the two worlds. Maybe they have to work together to fight a greater evil.
One idea could be that the vampires in Twilight somehow find their way into the wizarding world of Harry Potter. Maybe they are initially mistaken for dark creatures and there's a big misunderstanding. Harry and his friends have to figure out that they are not really a threat like the Death Eaters. They could then team up to fight a common enemy, like a new breed of dark magic - using the powers of both wizards and vampires.
Some crossovers could involve Harry's animagus form being used in a battle against the Volturi. His ability to transform quickly and his natural instincts as an animagus could give him an edge. Additionally, the Twilight characters might be fascinated by the concept of magic from the Harry Potter world. They could try to understand how Harry can change his form at will, while they are stuck with their vampire nature. There could also be a scenario where Harry uses his magic to help a Twilight character who is struggling with their vampiric existence, perhaps by using spells to ease their bloodlust or something similar.
Harry Potter himself could be a central character. His courage and ability to face dark forces could be put to the test in the Twilight universe. Maybe he has to deal with a vampire coven that has some dark intentions similar to Voldemort.