Yes. The kiss between Natsu and Lucy is a pivotal moment that adds depth to their relationship in the manga. It comes as a surprise to many but is a welcome development for their love story.
One common theme is the exploration of their unspoken feelings. Often, in the series, their relationship is somewhat ambiguous, and fanfiction allows for that to be explored more deeply with the kiss as a climax of those pent - up emotions.
Yes, there are quite a few. You can check out fanfiction websites like FanFiction.net or Archive of Our Own. Just search for 'Lucy and Natsu kiss' and you'll find a variety of stories written by different authors with different takes on their relationship.
They can develop their relationship by having small, everyday moments. For example, sharing breakfast together as a family, where they talk about their plans for the day. Natsu could show his love for Lucy by being more protective of her and their family in dangerous situations. Also, they could have inside jokes that only their family understands, which would strengthen their bond.