Well, you could have a plot where Edward discovers a new power within himself and we see his confusion and excitement through his pov. This could lead to him having to hide it from the other Cullens at first. Another idea is to write a fanfic about Edward's perspective on the werewolf - vampire relationship. He could be thinking about how it affects Bella and his family. Also, a story set in the future where Edward looks back at his life with Bella and all the challenges they overcame, with a lot of introspection on how their love has changed and grown over time.
For a 'Breaking Dawn Edward POV fanfic', you might consider his feelings about leaving Forks. He has such a strong connection to the place, and now with a new family member and Bella's transformation, he has to make the decision. You could write about his nostalgic moments, his hopes for the future in a new place, and how he deals with saying goodbye to the familiar. His conversations with Bella about this in his mind could add a lot of depth to the story.
One idea could be exploring Edward's thoughts during his first encounter with Bella in the cafeteria. How he was immediately drawn to her scent but also intrigued by her unique presence. Another could be delving into his internal struggle when he has to leave Bella to protect her, like the turmoil of his emotions and the self - loathing he might feel for putting her in danger just by being near her.
One interesting aspect is getting to see the story from Edward's perspective. We can understand his internal struggles with his vampire nature and his love for Bella more deeply. For example, his constant battle between his thirst for blood and his desire to protect Bella.
One interesting plot idea could be Renesmee growing up and facing the challenges of being a half - vampire in the human world. Maybe she tries to fit in at school but her special abilities keep getting in the way. Another could be Edward's struggle to protect Renesmee from the Volturi while also allowing her to have a normal life. For example, he has to decide how much to shelter her from the vampire world's politics.
A plot could involve Bella training in some ancient vampire magic that Edward doesn't know about. It could be a way for her to assert her independence and also help in the fight against their common enemies.
Another plot idea could be that Bella starts to have strange dreams during the honeymoon. These dreams seem to be prophetic, showing her glimpses of their future together and some potential threats. Edward tries to comfort her and figure out what these dreams mean, which could lead to a deeper exploration of their relationship and the Twilight world.
One idea could be that Bella discovers a new power that she and Edward have to figure out how to control together. It adds a new layer to their relationship and the overall Twilight -esque world they inhabit.
A 'pokemon pov fanfic' could be about a Charizard that was abandoned by its trainer. The Charizard's POV could show its feelings of betrayal, how it struggles to survive on its own in the wild, and its journey to find a new purpose or a new group of Pokémon to belong to.
One idea could be a story from the perspective of a minor character in the Twilight series, like a werewolf from a different pack who has an encounter with the Cullens. It could explore how they view the vampires and their relationships in Forks.
One idea could be a new vampire character arriving in Forks who has a unique power that disrupts the existing power dynamics between the Cullens and other vampires. For example, this new vampire might be able to manipulate time briefly, which could lead to some really interesting situations like preventing certain events from the original 'Twilight' series from happening or changing the way characters interact.