The themes of power and control are quite common. Peter has his werewolf powers and his own agenda, while the Sheriff has the power of the law in Beacon Hills. They might struggle over who has the real power in certain situations. Mystery is another theme, as they often have to solve strange occurrences in the town together. Their different perspectives - Peter's supernatural one and the Sheriff's more practical human one - add an interesting layer to the mystery - solving aspect of the stories.
Yes, there are quite a few. You can check out Archive of Our Own (AO3). There are many talented writers who create interesting stories about Peter Hale and Sheriff Stilinski. Some focus on their complex relationship within the Teen Wolf universe, like how they might have to work together despite their differences.
Some powerful and evil supernatural creatures could also be antagonists. For example, a powerful dark witch who wants to use Peter and Stiles for some dark ritual. She might try to manipulate them or put them in dangerous situations to achieve her goals.
One common trope is the 'unlikely alliance'. Given Peter's often - untrustworthy nature and Stiles' wariness, stories often start with them being forced to work together. Another is the 'protective Peter' trope, where Peter feels a need to protect Stiles for some reason. It could be because he sees Stiles' value to the pack or something more personal.
There's a fanfic called 'Unexpected Allies'. In this story, Stiles and Peter are forced to work together in a dangerous situation. It delves deep into their personalities and how they start to understand each other on a different level. Their interactions are really interesting to read about.
A more emotional storyline could be about Peter and Stiles forming an unlikely friendship. Stiles, who has always been a bit wary of Peter, gradually comes to understand him better and they develop a bond that helps both of them heal from their past traumas.
One great place to start looking for Peter Hale and Stiles Stilinski fanfiction is Archive of Our Own (AO3). There are numerous stories there with different themes and plotlines. Some might focus on their unlikely friendship, while others could explore a more romantic relationship between them. Just search for the tags related to 'Peter Hale' and 'Stiles Stilinski' on AO3, and you'll find a whole world of fan - created stories.
The contrast between their characters. Stiles is young, impulsive and full of heart, while Peter is older, more calculating. Their interactions can be really intense and full of chemistry.
There's a fanfiction called 'A Father's Love'. In this story, Sheriff Stilinski has to go to great lengths to protect Stiles from a powerful supernatural enemy. It shows their unwavering love for each other. Then there's 'Stiles and the Sheriff's Quest'. They embark on a journey together to solve a mystery that has haunted Beacon Hills for years, and their bond grows stronger throughout the adventure. Also, 'The Sheriff's Discovery' where the Sheriff finds out about Stiles' unique abilities and how to help him control them.
They're popular because it's an interesting dynamic. Stiles is a young, clever character and the Sheriff is an authority figure. Their relationship in the show has so many layers, and fanfiction allows fans to explore those layers further, like how they might support each other in different situations.