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.
There's also 'Unexpected Affection'. In this fanfiction, the kiss between Deku and Todoroki occurs in a very tense and emotional situation, like after a big battle where they realize their true feelings for each other. The author does a great job of building up the anticipation before the kiss.