Often, there is the theme of inspiration. Deku is very inspiring in the original story, and in fanfiction, he can inspire Shoto to be a better hero. Also, self - discovery. They both are on a journey to discover more about themselves, their powers, and their place in the hero world. In fanfiction, this journey can be elaborated on in different and interesting ways.
There are quite a few. 'The Adventures of Shoto and Deku' is a fun one. It takes them on various adventures outside of their normal hero school activities. It has a lot of character growth moments for both of them. Also, 'Shoto and Deku: A Shared Dream' is great. It imagines a future where they work towards a common, greater goal for the good of all heroes.
No way. The manga portrays their connection through mutual respect and competition in their journey to become great heroes. A kiss is not part of that narrative at all.
Yes, there are quite a few out there. You can start by looking on popular fanfiction websites like Archive of Our Own. Just search for 'Deku and Uraraka kiss' and you'll likely find some interesting stories.