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.
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.
I don't think it's a very common type. Most 'Harry Potter' fanfics tend to focus on the magical adventures, the relationships between the main characters like Harry, Ron and Hermione, or exploring different magical elements in the wizarding world. While there are some that might delve into darker themes, the idea of Petunia abusing Harry isn't as mainstream as other topics in the fanfic community.
Definitely. Fanfic writers often explore Petunia's role in Harry's life in a more positive light. Maybe she had some internal struggles about taking Harry in, not just out of spite but also out of fear of the wizarding world. Such fanfics can offer new insights into the 'Harry Potter' universe and its characters.
One possible fanfic could be about Petunia Dursley finding a magical toy that once belonged to Harry Potter's parents. Maybe she discovers it in the attic and it starts to show her memories of Lily and James Potter. She realizes that she has been wrong about Harry all along and decides to change her attitude towards him.
By focusing on their shared past traumas. For example, both have had experiences related to Lily's death in different ways. Harry lost his mother, and Petunia lost her sister. They could start to bond over this common pain and gradually move towards a more positive relationship.
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.
In a more comical plot, the lemon could be a mischievous magical object that keeps causing chaos in Petunia's house. It might make things float or turn into strange creatures. Petunia, being the uptight person she is, has to deal with this lemon - induced mayhem while also trying to keep up appearances in front of the neighbors. This could lead to some really funny situations and a change in her attitude towards the strange and magical over time.
A fanfic could connect them by having a toy that was passed down from Lily Potter to Harry, but Petunia has kept it hidden all these years. When Harry discovers it, it causes a big conflict as Petunia doesn't want to let go of the last piece of her sister she has in that way. But eventually, it could lead to a moment of reconciliation between them.
In the world of 'Harry Potter' fanfiction, most writers tend to stay within the boundaries of the original story's spirit. The concept of Harry Potter impregnating Petunia is so far - fetched and inappropriate that it is highly unlikely to be a part of any well - regarded fanfiction. Fanfiction usually focuses on exploring relationships that are more in line with the potential of the characters as presented in the original, like friendships, romantic relationships among peers, or the growth of the characters within the magical world.