There are indeed some. However, the quality can vary greatly. Some fanfics might depict Petunia as a more sympathetic single mother, showing how she copes with raising Dudley alone. Others may explore how her knowledge of the wizarding world (even if limited) affects her parenting. It's really a matter of exploring different works to find ones that suit your taste.
Yes, there are quite a few. You can start by looking on popular fanfic websites like Archive of Our Own. Some fanfics might explore a more complex relationship between Harry Potter and Petunia that wasn't fully shown in the original books. They could delve into Petunia's hidden feelings towards Harry, or how their relationship could have developed differently under certain circumstances.
One possible plotline could be Petunia struggling to make ends meet while raising Dudley on her own. She might have to take on extra jobs in the Muggle world, and this could lead to some interesting interactions with her neighbors. Another could be her dealing with Dudley's magical abilities (if he has any latent magic), which she has no idea how to handle.
Yes, there might be some out there. Fanfic writers often come up with unique and sometimes wild ideas. They might explore the idea of Petunia having some sort of connection to Harry in a way that involves babies, perhaps in an alternate universe or a what - if scenario. It could be about Petunia having a change of heart and taking in Harry in a more motherly way that could be related to the idea of new - borns or babies in a metaphorical sense.
One possible fanfic could be 'Petunia's Hidden Affection'. In this fic, Petunia's holding of infant Harry might be a turning point where she starts to feel a strange sense of protectiveness towards him. It could explore her internal struggle between her dislike for magic and her new - found connection to this magical infant.
Well, it depends on your definition of 'good'. Some might focus on the complex relationship between Petunia and the magical world in the context of Harry Potter, while others might take a more creative or off - beat approach. You really have to dig through different works to find one that suits your taste. There could be some that explore Petunia's character in depth, perhaps showing her envy of the wizarding world in a new light, or creating a scenario where she has a more positive interaction with the magical elements, which could be quite interesting to read.
Fanfiction.net is a great place to start. It has a large collection of 'Harry Potter' fanfics, and you can easily search for ones specifically about Aunt Petunia. Just type in 'Aunt Petunia' in the search bar and browse through the results. You might find some real gems there.
One great Petunia fanfiction could be one where she has a moment of self - realization. Maybe she discovers some of Lily's old magic things and starts to understand the wizarding world better. It could show her in a more sympathetic light, perhaps she even tries to protect Harry in her own way.
One interesting 'Harry Potter Petunia Dursley' fanfic could be one that explores Petunia's childhood and how her relationship with Lily might have affected her view of Harry. For example, a fanfic could show that deep down, Petunia was always a bit envious of Lily's magical abilities, but also loved her sister in a complicated way. This envy could have then translated into her cold treatment of Harry.
One interesting 'Harry Potter Aunt Petunia' fanfic could be the ones that explore her relationship with Lily before she passed away. It might show how they grew up together and how their bond changed over time. Maybe there are fanfics where Aunt Petunia has to face her own insecurities regarding magic and her sister's special abilities.
Fanfiction can cover a wide range of themes, but 'Harry Potter x Petunia' with a 'lemon' aspect is not something that aligns well with the overall tone of the original story. The series is mainly about magic, friendship, and the fight against evil. If you're interested in their relationship, look for fanfictions that explore their family dynamic, like how Petunia's jealousy and fear influenced her treatment of Harry, rather than 'lemon' ones.