There is some. However, the quality can vary a great deal. Some might focus more on the emotional connection between Itachi and Hinata, while others might add more action or adventure elements into their relationship. It really depends on what you're looking for in a fanfiction.
Sure, there are. These fanfictions often explore unique relationships that are not part of the original Naruto storyline. Writers get creative and might imagine how Itachi and Hinata could interact in different scenarios, such as in an alternate universe where they meet under different circumstances. It's interesting to see how different authors develop their relationship in their own ways.
Yes, there are quite a few. You can check out fanfiction websites like FanFiction.net or Archive of Our Own. Just search for 'itachi and hinata' in the search bar and you'll find a variety of stories with different plotlines and writing styles.