I'm not sure of a specific one off - hand, but you can start by looking on popular fanfiction websites like FanFiction.net or Archive of Our Own. Search for 'Natsu Prince of Alvarez' and look at the ratings and reviews of the stories to find a good one.
One interesting fanfiction could be about Natsu's adventures in Alvarez as a prince. Maybe he has to face some political intrigue within the kingdom. Another could focus on his relationships with other characters from the original series in this new 'prince' context. For example, how his friendship with Lucy might change or develop in this Alvarez royalty setting.
Yes, there might be such fanfictions out there. Fanfiction writers often come up with unique and creative ideas like this. They might explore how Natsu's hidden identity as a Dragon Prince could impact his relationships with his friends in Fairy Tail, or how it could change the power dynamics within the story. It could lead to all sorts of interesting plot twists and character developments.
Obviously, Natsu is one of the main characters as it's in the title. He is likely to be the central figure around which the story revolves. There might also be other dragons that play important roles, like his dragon family members if they are introduced in the fanfiction.
One common theme is her relationship with other characters. Many fanfictions explore her friendships or potential romances. For example, her dynamic with certain side characters can be a central focus.
Some Tumblr blogs might also feature or recommend 'natsu is a dragon prince fanfiction'. You can search for relevant tags like #natsu #dragonprince #fanfiction. It's a bit more of a scattered search compared to the dedicated fanfiction websites, but you might discover some hidden gems that way.
Some fanfictions could focus on Natsu's journey to discover his true dragon prince heritage. This might include him facing challenges that are unique to his royal bloodline, like unlocking special dragon powers that were previously hidden from him. For example, he might learn to communicate with ancient dragons in a way he couldn't before.
One interesting storyline could be Natsu's journey to discover his true dragon heritage in a more in - depth way. Maybe he uncovers secrets about his dragon family that were previously unknown. Another could be his adventures in a new dragon - ruled realm where he has to prove himself as a prince.
I really like the Alex Alvarez fanfiction in the context of One Day at a Time. It often brings out new aspects of his character. The fanfic writers manage to explore his relationships and personal growth in ways that the show might not have fully delved into. It's interesting to see how different writers interpret his character and the situations he could be in.