Yes, there are quite a few. You can start by looking on fanfiction websites like FanFiction.net or Archive of Our Own. Just search for 'gaara and sakura dating' and you'll find a variety of stories with different plotlines and writing styles.
Sure, there are many out there. Fanfiction often takes the characters from the Naruto universe like Gaara and Sakura and gives them new storylines. In these 'gaara and sakura dating' fanfictions, you could see their relationship develop in ways that were not shown in the original anime or manga. For example, some might show how they overcome cultural differences (since Gaara is from Suna and Sakura is from Konoha) while dating, or how they deal with the reactions of their friends and comrades to their relationship.