Another appropriate way is to explore her backstory. Perhaps write about her days as a student at Hogwarts, what made her interested in Transfiguration, and how she overcame challenges in her own academic journey. This would give more depth to her character without being inappropriate.
Definitely not. She is a respected figure in the wizarding world. Fanfiction should focus on positive aspects like her leadership, teaching skills, and her role in the Hogwarts community rather than creating inappropriate content about her.
You can focus on their mentorship relationship. Minerva could be guiding Hermione in her academic pursuits or in dealing with the challenges within Hogwarts. For example, Minerva could help Hermione master a particularly difficult spell or give her advice on how to handle a tricky situation with other students.
You can focus on her adventures with The Doctor. For example, write about a new planet they visit together, the challenges they face there, and how they overcome them using their unique skills and the bond between them.
An appropriate fanfic could be centered around her friendship with other musicians or her interactions at music events. For example, you could write about her collaborating with other artists in a positive and creative way.
You can write fanfic that focuses on her characters' adventures in the shows or movies she has been in. For example, if she played a superhero, you could write about her character's heroic deeds and how she saves the day.
You can write about his characters in different scenarios that are in line with the storylines of the shows or movies he has been in. For example, exploring how his character might react in a different plot twist.
A great way would be to write about her friendships with other characters in the shows or movies she has been in. Maybe a story about how she helps a co - star overcome a difficult situation in the fictional world they inhabit together. This kind of fanfic is positive and respects her as an artist.
You can focus on their friendship. Maybe write about how they first met and how their initial interactions led to a deeper bond.
You can focus on her adventures in solving mysteries. For example, you could write about her investigating a strange occurrence in her school or neighborhood. This would stay true to her inquisitive nature.
One appropriate way is to focus on her political journey. For example, you could write about how she navigates the complex political landscape of Westeros, her relationships with other political figures, and how she uses her intelligence to gain power and influence.