Often, Hermione is shown as the intelligent and determined one. She might be the driving force behind solving a problem that involves Draco and the professors. The professors can be portrayed in different lights. Some fanfictions might show Snape as having a more sympathetic side when dealing with Draco and Hermione's situation. And Draco may be seen as a complex character who is trying to redeem himself in the eyes of the Hogwarts community, which includes the professors.
One interesting storyline could be a time - travel plot where Hermione and Draco are sent back in time and have to work with Hogwarts professors from different eras to fix a major magical disruption. For example, they might have to team up with Professors Dumbledore and Snape in the past to prevent a dark wizard from changing the course of wizarding history.
It's not appropriate at all. The Hogwarts professors are respected figures in the wizarding world created by J.K. Rowling. Creating fanfiction with sexual content about them goes against the values of the original series. It also may make many fans of the series uncomfortable as they view these characters in a different, more positive and educational light.
In some ways, it could be seen as positive. Hermione is a complex and beloved character. Professors might desire Hermione fanfiction because it can offer new insights into the character, different from what's in the original books. For example, fanfictions might explore her life after Hogwarts in ways the official series doesn't. But they still need to maintain appropriate boundaries as educators.
It would change a great deal. First off, McGonagall would probably be more involved in Hermione's academic progress on a personal level. She might give her special assignments or extra tutoring. As for the other professors, they might view Hermione as having an 'inside track'. For instance, Professor Flitwick could be more lenient with her in Charms class. This new dynamic would add a whole new layer to Hermione's Hogwarts experience and how she interacts with the faculty.
The students would likely gossip a great deal. The news would spread like wildfire through the corridors of Hogwarts. Some students might be more open - minded and see it as a chance for a new kind of unity between houses. But many would be judgmental. The Hufflepuffs and Ravenclaws would also have their own views. Hufflepuffs might be more empathetic towards Draco and Hermione, while Ravenclaws might analyze the situation from all angles, trying to figure out how such a thing could have happened in the first place.
One common theme could be redemption. Draco might be seeking redemption for his past actions, and Hermione could be the one to either grant it or help him achieve it. Another theme could be forgiveness. They have to forgive each other for all the bad blood between them over the years.
In the fanfiction, there could be a mystery at Hogwarts that brings them back together. For example, a dark magic artifact that was hidden long ago resurfaces. Draco, with his Slytherin knowledge of the castle's secrets, and Hermione, with her vast research skills, team up to solve the mystery. Along the way, they discover new things about each other and themselves, and perhaps even develop some romantic feelings, though it would be a very unexpected and complex relationship given their past.
One negative impact is that it can corrupt the image of the Hogwarts professors. They are supposed to be role models in the wizarding world. Also, it can be very disturbing for the young fans of the Harry Potter series who look up to these characters.
Well, in fanfiction, it's often about bending the rules. Maybe it could be some sort of magical accident. For example, a misfired spell that had some unexpected consequences on their relationship and led to this situation.