Well, 'Petunia's New Path' is a great fanfiction in this regard. In it, Petunia discovers a magical object that gives her insights into Harry's world and makes her more empathetic. She starts to show small acts of kindness, like leaving a warm drink for Harry when he comes home from Hogwarts. Another fanfic, 'The Nicer Petunia', shows her being kind to Harry during the summer holidays. She might take him shopping for new clothes or listen to his stories about Hogwarts without being dismissive.
One such fanfiction could be where Petunia finally accepts Harry and his magical world. She might have a change of heart after seeing how much Harry has suffered. This could lead to her helping Harry in some way, like using her knowledge of the Muggle world to assist him in a difficult situation.
One good Petunia - related fanfiction could be 'Petunia's Secret'. It delves into Petunia's hidden emotions and her complex relationship with the wizarding world. In this fanfic, it might show how she really felt about Lily's magical abilities all along and her internal struggle with envy and love for her sister.
Sure. 'Petunia's Perspective' is a great one. It gives a unique view from Petunia's point of view, which we rarely see in the original books. It shows how she saw the comings and goings of wizards in her life and how it affected her view of her family and the world around her.
Definitely. In certain fanfictions, Petunia's nice side is revealed. Maybe she has a change of heart after some events. For example, she could start to understand Harry better and show kindness towards him. These fanfictions often rewrite parts of the story to give Petunia a chance to redeem herself and be a more positive character in Harry's life.
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.
Fanfiction.net is another great place. It has been around for a long time and has a lot of 'Harry Potter' fanfictions. When you search for Aunt Petunia - related ones, make sure to read the summaries and reviews to get an idea of which ones are good. Some might be more focused on her backstory, while others might explore her relationship with other characters in new ways.
There are fanfictions where Aunt Petunia has a change of heart towards Harry much earlier in the story. Instead of treating him badly, she starts to secretly teach him some basic things about the wizarding world that she learned from her sister Lily before she passed away. This could add a whole new dynamic to Harry's early years at the Dursleys.
There are fanfictions where Petunia has a change of heart towards Harry. For example, she realizes the error of her ways after seeing how much danger Harry is constantly in at Hogwarts. She then tries to make amends by secretly helping him, like sending him care packages with useful Muggle items that can be adapted for magical use.
I'm not sure if there are 'popular' ones in the sense that they are widely known and accepted. Lemon fanfictions are a bit of a niche and often not mainstream due to their mature content. But there might be some that have a following within the more hardcore Harry Potter fanfiction community.
There could be a fanfiction where Petunia Dursley discovers some hidden magic within herself and this somehow links her more closely to Harry. In this scenario, the story could take on a whole new dimension. But as for a particular 'Harry Potter and Petunia Dursley lemon fanfiction', it's hard to point out one without really searching through various fanfiction sites. Also, remember that lemon content often implies sexual undertones which may not be appropriate for everyone.