One common theme is the exploration of a forbidden love, as there could be various reasons in the story's universe that make their relationship not straightforward. Another theme is the discovery of shared secrets or powers that bind them together.
Yes, there are quite a few. You can start by looking on popular fanfiction websites like FanFiction.net or Archive of Our Own. Just search for 'natsu x layla heartfilia' and you'll find a variety of stories. Some might be more to your taste in terms of writing style and plot development than others.
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 adventure. Natsu and Lucy often go on quests together in fanfics, facing various challenges. Another theme is love. Their relationship, whether it's budding or fully developed, is a central focus. And friendship is also important. They are part of a guild, so their bond as friends within the group and specifically between them is often explored.
One aspect of their married life in fanfiction could be the domestic side. Lucy might try to get Natsu to be more organized at home, while Natsu would bring his energetic and fun - loving nature into their household. They would probably have a lot of cute and comical moments, like when Natsu accidentally burns the dinner and Lucy just shakes her head and laughs it off. Their love would continue to grow as they share these everyday experiences.