One common plotline could be Bella getting injured in a way not shown in the original Twilight series and Edward being overly protective in the hospital setting. For example, she might be in a car accident on her way to visit Jacob and end up in the hospital. Edward would then be by her side constantly, causing some tension with the werewolf pack who also want to check on her.
Edward, of course. He's Bella's main love interest in the Twilight series, so it's very likely he'll be by her side in the hospital. He would be the one to comfort her, and his vampire abilities might come in handy, like his super - speed to get things she needs quickly.
A doctor named Dr. Smith could be a main character. He could be a strict but fair physician who at first doubts Bella's abilities but later comes to respect her.
Often, the Cullens are main characters in Twilight hospital fanfiction. Since they are vampires, they might interact with the hospital in various ways, like bringing in a human they want to protect or dealing with a situation where their vampire nature is at risk of being exposed in a medical setting.
One interesting Twilight hospital fanfiction could be about a vampire getting injured and having to be secretly treated in a human hospital. The staff might be in for a big shock when they realize the patient's unique condition.
Yes, there are some out there. You can start by looking on popular fanfiction websites like Fanfiction.net or Archive of Our Own. Just search for 'Twilight Bella is a werecat' and you'll likely find a variety of stories with different takes on the concept.
One idea could be that Bella is a new nurse in the hospital and she discovers a secret patient who has a mysterious illness. She then teams up with a brilliant but reclusive doctor to try and solve the mystery.
In 'Saving Bella' fanfiction, it might involve a unique take on rescuing Bella from various perils. Maybe it's a different vampire or werewolf who steps in to save her from a danger that the original story didn't cover. For example, it could be a new character who has a special power or knowledge that enables them to keep Bella safe from a hidden threat in Forks.
In some fanfictions, Jacob and Bella's pregnancy can take on various plotlines. One possibility is that it creates a huge rift between the werewolf pack and the Cullens. Jacob's loyalty to Bella is tested as he tries to protect her and their unborn child from the potential threats in the Twilight world, like the Volturi. This situation often leads to a lot of drama and tension in the fan - created stories.