In some fanfictions, his fall off the broom could be a turning point in the story. It might lead to him discovering a new magical ability. For instance, he could unconsciously use a form of magic to slow his fall or even levitate himself slightly. This newfound ability could then be explored further in the story, perhaps making him a more powerful wizard in unexpected ways.
In certain fanfictions, Harry's fall could be a part of a larger conspiracy. Maybe someone tampered with his broom on purpose. This would then lead to an investigation, with Harry and his friends trying to figure out who was behind it. Along the way, they could uncover other secrets about Hogwarts or the wizarding world in general, which would add more depth and complexity to the plot.
He could get seriously injured. In some fanfictions, he might break a bone or two. It would also likely lead to him being out of the Quidditch match if it happened during one.
Dumbledore could also be a savior. Given his powerful magic, he could easily appear at the scene and use a spell to stop Harry from hitting the ground too hard. Or perhaps one of the teachers at Hogwarts, like Professor McGonagall, who is strict but caring, would use her transfiguration skills to create something to break his fall.
A plot twist could be that when Draco falls off his broom, instead of Hermione helping him directly, she uses a spell to make his broom catch him at the last moment. This shows her intelligence and also makes Draco question her motives. Later, he discovers that she didn't want to expose their growing friendship to others. Another twist could be that Draco's fall was actually a planned thing by someone who wanted to harm him, and Hermione has to figure out who it was while taking care of Draco. This adds a mystery element to the story.
Definitely. There are fanfictions that explore the relationship between a character and their broom in a platonic and magical way. For instance, a story could be about how a character discovers an old, forgotten broom in the attic of Hogwarts and then uncovers its hidden powers and history, which is a much more positive and appropriate take compared to inappropriate ideas.
No. The official Harry Potter universe is mainly focused on magic, friendship, and the battle between good and evil. There is no such inappropriate concept as 'harry potter sex with a broom' in the original works. J.K. Rowling created a magical world for all ages, especially for children and young adults, with positive values and themes.
There are several interesting ideas. For instance, a fanfiction could focus on the broom's history. Maybe it was once owned by a great wizard in the past and has some latent powers that Harry gradually uncovers. Another idea is that the broom could be the target of a dark wizard's plot, and Harry has to protect it. Also, a story could be written about how Harry uses his broom to explore areas outside of Hogwarts that are normally off - limits, and the adventures he has during those explorations.
One interesting 'Harry Potter Broom Closet' fanfiction could be one where the characters use the broom closet as a secret meeting place to plan pranks on the Slytherins. They might stock it with all kinds of magical items for their schemes.
One possible reason could be to protect himself from the pain and loss he has endured. After all he's been through, like the death of his parents, Sirius, and so many others, turning off his emotions might seem like a way to avoid further hurt.