There are quite a few out there. You can start by looking on fanfic websites like Archive of Our Own. Just search for 'Sly x Carmelita kiss' and you'll find a variety of stories with different takes on their relationship.
Yes, there are some. However, the quality can vary greatly. Some might focus more on the action and adventure aspects of Sly's world and just have the kiss as a sweet moment, while others might be more centered around their relationship development leading up to the kiss.
There are. But it really depends on what you're looking for in a fanfic. If you like a more comical take, you might find ones where the kiss is a result of some wacky misunderstanding. If you prefer a more serious and romantic approach, there are those as well. You just have to dig through the fanfic archives to find the perfect one for you.
A practical answer is Chapter 18, because it turns the idea into a concrete scene. The chapter opens with In the corner, a girl in a black dress sat quietly, holding a glass of..., adds pressure through I have no reason to joke with the rest of my life." "Moreover, I wouldn't..., and ends on Hurry.
Chapter 808, "Dare to Spank Him?!", is the clearest early answer because it turns Jiang Buchen's situation into a concrete plot event. It opens with I don't listen, I don't listen," Jiang Bufan once again started his...
A practical answer is Chapter 4, because it turns the idea into a concrete scene. The chapter opens with Qiao regretted her words as soon as they left her mouth., adds pressure through It's difficult for us when you ask for a guest's room number and key right..., and ends on A little girl acting.
The best chapter pointer here is Chapter 31, "Master, I've been having some bad luck lately!". It opens with Before Shen Lan had reached the backyard, she already heard the sounds of... and closes on After staying in the study and reading for another day, she finally....
The best chapter pointer here is Chapter 21, "Uncle Policeman, They Are the Ones Causing Trouble!". It opens with Jiang Li's clear and logical explanation had everyone stunned in place. and closes on But the implications could be different..
Chapter 4 is the strongest chapter-level answer because it starts from Qiao regretted her words as soon as they left her mouth. and follows through on A little girl acting mysterious, learning fortune-telling, what is this....
Chapter 702, "This is One Hundred Million, Sign Here!", is the clearest early answer because it turns Wu Daoshan's situation into a concrete plot event. The chapter turns that into something concrete by moving from Bai Lu was at a loss for words.
A practical answer is Chapter 17, because it turns the idea into a concrete scene. The chapter opens with Jiang Li glanced at Jiang Shixu, who was tense and anxious behind her, and..., adds pressure through That girl who puts on makeup like a ghost deserves to be called naturally..., and ends on.
Chapter 760, "Daoist, I've Long Heard of Your Great Reputation", is the clearest early answer because it turns Long Heard's situation into a concrete plot event.
Chapter 867, "Then what does our child count as?!", is the clearest early answer because it turns Jiang Li's situation into a concrete plot event.