Yes, there are likely fanfictions out there with such a plot. Fanfic writers often explore different and sometimes controversial storylines. However, this goes against the strong bond between Sasuke and Naruto in the original series.
It could be due to some fans' different interpretations of the characters. Maybe they see a certain chemistry between Sasuke and Karin in the original series that they want to explore further, even if it means creating a scenario where Sasuke cheats on Sakura. Also, fanfiction is a place for creativity and exploring different possibilities, and this is just one of the many extreme or different ideas that can come out of that.
There could be. The world of fanfic is vast and diverse. Some writers might create stories where Sakura cheats on Sasuke to add drama, explore different character dynamics, or simply as an alternative universe scenario. But it's important to note that this is not in line with the main Naruto narrative.
It's possible that such a fanfic exists. The world of fanfiction is full of all kinds of creative and sometimes unexpected interpretations. Some writers might want to break the mold and show Sakura and Sasuke in a less than ideal light to explore different storylines or character developments. But it's not something you'd find easily among the more popular fanfics.
Naruto would probably be deeply hurt. He values his relationship with Sasuke so much that such a betrayal would shatter him. He might become withdrawn or angry.
I'm not sure if there is such a specific fanfic. Fanfic topics can be extremely diverse, but this particular scenario seems rather untrue to the original Naruto storyline and the relationships established in it. However, in the vast world of fanfiction, almost any idea can be explored, so it's possible that someone might have written it.
In this fanfic, it could even be her best friend's partner who has been secretly interested in Sakura and cheats on her best friend with Sakura. This would add an extra layer of drama and betrayal as it not only affects Sakura's relationship but also her friendship.
I'm not entirely sure if it's a 'popular' trope. Some fans might be interested in exploring such dramatic and controversial storylines in fanfiction for the shock value or to explore different character dynamics. However, many fans of the original Naruto series who ship Sasuke and Sakura would likely be disappointed or even offended by such a concept.
A great theme could be their training together. They could learn new jutsu from each other and grow as ninjas. This would show their mutual respect and the bond they form through their shared goals.
Sasuke could initially be a vampire who is full of anger and resentment, maybe because of how he was turned. But Sakura's positive attitude and kindness could start to soften him. He might start to open up about his past and his feelings. Sakura could develop from a somewhat naive vampire into a more worldly and wise one. She would learn about the darker side of the vampire world through Sasuke, and this would change her. Maybe she would become more cynical at first, but then find a balance between her old self and the new knowledge she has gained.