One possible theme could be the fear of the unknown. If Takagi san is placed in an unfamiliar and spooky situation, like a dark forest at night, this theme would be prominent. Another theme might be betrayal. Maybe someone she trusts turns out to be a part of the horror she faces.
If the 'Takagi san scary story' is a fan creation, it might draw on the existing characteristics of Takagi san and transform them into something scary. For example, her usually cheeky and teasing nature could be turned into something more menacing in the horror context. It could also be that in this story, she gets involved in a mystery that has a terrifying solution, but again, without more details, it's all guesswork.
Well, generally speaking, Takagi San Visual Novel probably centers around the characters from the Takagi - san franchise. It may present different storylines that explore the personalities of Takagi and other characters more deeply. Maybe it has mini - games or choices that can lead to different outcomes related to their relationship, like whether Nishikata can finally get the upper hand in their teasing battles.
One popular Takagi San fanfic could be those that explore their future relationship. For example, fanfics where they are in high school and facing new challenges together while still maintaining their cute interactions. Another good type might be the ones that fill in the gaps between the episodes, like what they did during a short break not shown in the anime.
There are fanfictions that might explore alternate universes. For example, a Takagi san fanfiction where they live in a world full of magic. Takagi could use her wits in a different way in this magical setting, and Nishikata would have to adapt too. Also, some fanfictions could be about their childhood before the events in the original story, showing how their relationship started to form in those early days.
Takagi is a main character. She is a smart and mischievous girl who likes to tease Nishikata. For instance, she always comes up with clever ways to make Nishikata blush or get flustered.