I am strictly referring to the books, not the movie. The movie made the characters extremely shallow, and you don't see enough about them to type them. There's so much more depth to them in the books.
I think in Twilight and New Moon Bella was an INFJ, then Stephenie accidentally "switched" her type to an ISFJ in Eclipse and Breaking Dawn. It was like Bella had a personality transplant from the first half of the Saga to the second half. (This is possible because they're fictional characters, and entirely how the author writes them.) If you read the books, Bella is in no way a P. She's always planning, saving money, doing her homework in a timely fashion (I doubt she's pulled an all-nighter.) And the whole plan in Breaking Dawn with Jenks was a very J thing to do.
I'm not really sure he has a concrete personality, as he's written to be ideal for anyone who reads the book. He always wants to do the best for Bella, but can't really see what's best for her. He is in tune to what other people feel/think/what's going on with others (thus his power to read thoughts) so I would definitely place him as an F. He also has difficulty seeing how what he does will affect others; he only thinks about the moment and doesn't understand the long-term consequences of his actions.
This seems right; the only problem is that Alice has an extremely high Ni (which manifests in her power.) Otherwise, she's extremely ENFJ.
He's completely Fi. He obviously has a very rich inner world, evident when he finally opens up to Bella about his life in the south. He's also quite impulsive (it's only because of Alice that he curtails his desire for human blood). Him and Alice have this epic romance thing going on, and his intense emotional depth is barely covered, even in the books.
If you read the description and all four books, this seems like the best fit. She's not naturally in tune with her emotions (thus the whole Royce King event), and is very obligated to fulfilling her duty. (Especially with having children and helping Bella with the pregnancy.) She is a perfectionist and extremely loyal to her family.
He wavers sometimes between T and F, but I think he's a T. This one is hard! He's definitely mechanical and a fan of extreme sports. Very live in the moment, and definitely a P. I also think he's an I, because when he needs time to recharge or think he turns into a wolf and spends alone time running in the forest, or disappearing altogether. He's personable, but doesn't need others the way an E does.
Renesmee: ESFP! lol
Interesting pattern... the majority of Stephenie's characters tend to be feelers. Perhaps she is a feeler herself?