Often, there are themes related to family. Maybe exploring Addie's relationship with her family members, like her parents or siblings. Romance can also be a big theme. Writers might create love interests for Addie and write about their budding relationships. There could also be themes about overcoming challenges, where Addie has to face difficulties and grow from them.
You can try fanfiction platforms like Archive of Our Own (AO3). It has a large collection of fanfics from various fandoms, and there's a good chance you'll find some great Addie McCallister fanfic there. Another option could be FanFiction.net, though AO3 generally has more diverse and inclusive content.
Perhaps there's been some sort of miscommunication or misunderstanding among Peter and his friends. Maybe a villain has manipulated the situation in such a way that his friends now think Peter has betrayed them, so they've cut off all ties with him. This would create a very lonely and difficult situation for Peter in the fanfiction.
Peter could be just an ordinary person with an extraordinary love for dogs. He might be a local boy who has always been fascinated by the tower and decides to bring his furry friends along on his adventure.
Peter could be a disgruntled noble in the fanfiction. He might be someone who has been overlooked for promotions or honors by the emperor, and this has led to his resentment and desire to kill the emperor.
Again, without more context, it's hard to say exactly who Peter Braestrup is in this 'big story'. He could be an author, an activist, or someone who made a mark in a particular industry.
The story behind 'Peter Peter Pumpkin Eater' is kind of mysterious. Nobody really knows for sure how it came to be. It's just one of those rhymes that has always been there, without a detailed explanation of its origins.