If Bella was a mermaid - like creature, her relationships with both the vampires and werewolves would be on a different level. She would be tied to the ocean and have her own underwater world to deal with. The vampires and werewolves might be curious about her world, and Bella would have to balance her new identity with her previous connections, which would make for a very complex set of relationships.
As a non - human, say a powerful witch, her relationship with Jacob would also change. Jacob might be more in awe of her powers and less likely to try and win her over in the same way. Bella could use her magic to either help or hinder the werewolves, which would create a new dynamic in their relationship.
If Bella were a vampire from the beginning, her relationship with Edward would be different. They would be equals in terms of strength and immortality. There might not be the same level of protectiveness from Edward as he wouldn't need to worry about her being so fragile. Their relationship could be more of a partnership in the vampire world.
Their relationship would likely become more intense. Edward would be more protective of Bella. He might constantly worry about her well - being and that of the baby.
If Bella becomes a banshee, her relationship with Edward would be very different. He would be more protective of her as she has a new and potentially dangerous power. He might also be a bit wary as banshees are known for their wailing which could attract unwanted attention. With Jacob, he might see her as even more of an enigma and be more drawn to her in a way, since she's now a more powerful supernatural being.
If Bella is not human in fanfic, the love triangle dynamic changes. For instance, if she's a vampire, her relationship with Edward might be more of an equal power - based relationship rather than the human - vampire dynamic in the original. And her connection with Jacob would be less about protecting her as a human.
Her relationship with Bella would likely become more complex. As a vampire, she would have different needs and instincts. She might be more protective of Bella in a way that Bella doesn't understand at first. For example, she could sense danger towards Bella that a human wouldn't notice. But at the same time, Bella might be a bit afraid of her sister's new vampire nature, which could create some tension between them.
If Bella was Carlisle's daughter, her relationship with the other Cullen siblings would be altered. She would be part of the family in a more fundamental way. For example, Alice might see her more as a sister to protect and guide, rather than just a friend. And Rosalie might have a different attitude towards her, perhaps being more accepting since she is Carlisle's daughter. Jasper could also be more involved in her training or development as a vampire, as he has his own skills and experiences to share.
It would become more intense and complex. Jacob would be very protective, his werewolf instincts kicking in fully. He'd be constantly worried about Bella and the baby's safety.
The story would change a great deal. For starters, Bella's initial perception of vampires would be different as she would grow up with Esme, a vampire. She might not be as scared or intrigued by them. Also, the Cullen family dynamics would shift. Esme would be more protective of Bella within the family, and there could be less of the initial mystery and tension between Bella and the Cullens. Edward's relationship with Bella might also develop differently, as Esme would play a more direct role in their interactions.
It would change the love triangle aspect completely. Instead of Edward - Bella - Jacob, it would be Jasper - Bella. This would lead to different interactions between the characters. For instance, Jacob might not be as involved in Bella's life as he was in the original story. The focus would shift from Edward's attempts to protect Bella from his vampire nature to Jasper's way of dealing with it. And the Cullen family's reactions to this new pairing would be a major part of the story.
If Bella was pregnant by Alice in fanfiction, it would introduce a whole new set of conflicts. The Volturi would likely view this as a threat to the vampire order. Bella's pregnancy would be a sign of something that goes against their understanding of vampire nature. As for the characters, Alice would have to reevaluate her life and role. Bella would be in a world of trouble, not just from the vampire side but also from her own human side. Her father would be clueless about what was going on, and she would have to keep this huge secret. It would be a story full of secrecy, conflict, and a need for acceptance.
The story would change drastically. First, the love triangle would take on a whole new meaning. Edward's love for Bella might be challenged by his vampire nature's aversion to werewolves. Bella's friendship with Jacob would also transform. They would be pack mates now, and their relationship could become more complex. Second, Bella's role in the Forks community would be different. As a werewolf, she'd be more involved in the supernatural side of things, perhaps having to keep her new identity a secret from more people than just the Cullens.