Well, a very frequent theme is self - discovery. 'That girl' may be in a situation where she has to figure out who she really is, especially when she's thrust into the strange and often dangerous world of Twilight. Also, friendship is a common theme. She might form strong bonds with the existing characters, and these friendships could be crucial in the development of the story. There can also be themes related to power and control, as in the struggle between the vampires and werewolves in the Twilight universe, and how 'that girl' fits into that struggle.
Yes, there are quite a few. You can check some fanfiction websites like FanFiction.net or Archive of Our Own. Just search for 'that girl twilight' on those platforms and you'll find a variety of stories written by fans, ranging from romantic takes on the Twilight characters to new and unique plotlines involving the concept.
Well, it could also be about how the wolf character is developed in the fanfiction. Maybe it gives more backstory to the wolf, his motives, and how he interacts with the girl in different situations. For example, does he protect her more fiercely than in the original? Or does he have some inner conflicts related to his feelings for the girl that the fanfiction delves into?
A common theme is discovery. The little girl often discovers the secrets of the Twilight world, like the existence of vampires and werewolves. It's a journey of her coming to terms with the extraordinary things around her.
One interesting 'The Little Girl' Twilight fanfiction could be about a little girl who discovers she has a special power in the Twilight universe. For example, she might be able to communicate with the wolves in a way no one else can. This could lead to all sorts of adventures and her becoming an important part of the story's fabric.
She could be a long - lost relative of one of the Cullens. Maybe she was turned into a vampire long ago and has been living in isolation. The red umbrella is a memento from her human life, and now she's coming back into the Cullen family's orbit.
Friendship is a common theme. A little girl in the fanfiction might form a special bond with Bella or one of the Cullen family members. Another theme is the idea of magic and mystery. Since Twilight has vampires and werewolves, the fanfictions often explore how a little girl reacts to these elements.
I'm not sure specifically as there could be many interpretations. It might be about a new girl in a story related to 'Twilight' and someone's mate. Maybe it's a fan - created story where this new girl disrupts or changes the relationships in the 'Twilight' universe.