It could be Dumbledore. He might have realized that the Dursleys were not the best place for Harry after all and decided to take matters into his own hands, using his powerful magic to rescue baby Harry.
One possible scenario could be that a powerful wizard or witch, perhaps someone who knew James and Lily Potter well, comes to rescue baby Harry. They might use magic to bypass the Dursleys' defenses and take Harry away to a safer place, like a hidden wizarding community.
In this kind of fanfiction, perhaps Harry is rescued by the Order of the Phoenix earlier than in the original story. They might have realized the Dursleys' mistreatment sooner. Then Harry could start his magical training earlier, away from the hostile environment of the Dursleys' home. He may also form closer bonds with other members of the Order, like Sirius, who could play a more active role in his upbringing.
Hermione could be the rescuer. Maybe she discovers through her research that Harry is in a bad situation at the Dursleys' and decides to take action. She uses her intelligence and magic skills to break into the Dursleys' house and get Harry out. Then they would go on an adventure together, and Hermione would be like a mentor to Harry in a way, teaching him things she has learned from books.
Perhaps Harry is rescued by an unexpected character, like a centaur who has been secretly watching over him. The centaur arrives at the Dursleys' on a moonlit night, and using its natural magic and knowledge of the stars, it convinces Harry to come with it to a safe place in the Forbidden Forest where he can be protected and trained.
Obviously, Harry Potter is a main character as the story is centered around him as a baby at the Dursleys. Then there are the Dursleys themselves - Vernon, Petunia, and Dudley. Vernon is the strict and often cruel uncle, Petunia is the conflicted aunt who has her own issues related to the wizarding world, and Dudley is the spoiled cousin.
One interesting plotline could be Harry showing early signs of magic that the Dursleys try to suppress. For example, he might accidentally make Dudley's toys float when he's angry or frustrated.
There are indeed. A lot of fanfiction writers like to take the concept of the Dursleys being kind to baby Harry and run with it. They might write about how the Dursleys initially had good intentions but got corrupted by their fear of magic later. Or they could create a scenario where the Dursleys truly care for Harry from the start, changing the whole dynamic of the early Harry Potter story. It gives a fresh perspective on the characters.
Well, family unity is often a theme. Since the Dursleys love baby Harry, it creates a more harmonious family environment. This is different from the original story where Harry was mistreated. Also, the exploration of how this love affects Harry's magical abilities and his relationship with the wizarding world is common. For instance, he might be more open about his magic to the Dursleys, and they in turn support his journey in the magical realm.
There are fanfictions where a powerful wizard or witch, not part of the main Hogwarts faculty, discovers Harry's situation. Maybe an old hermit wizard who lives on the outskirts of the wizarding world. This wizard uses his magic to create a diversion at the Dursleys' place and then whisks Harry away to his own hidden cottage where he teaches Harry different kinds of magic not taught at Hogwarts.