It depends on how you define 'popular'. There are a lot of Twilight fanfictions out there, and this particular theme might not be the most common. However, within certain subsets of the fanfiction community, it could be quite popular. For example, fans who are interested in exploring power dynamics and the darker side of the characters might be drawn to this type of fanfiction. It also might appeal to those who want to see Bella in a more vulnerable position and how she would react to being bullied by the Cullens, which is a departure from the typical story where she is often the center of their affections.
One common plot point could be the Cullens isolating Bella at school. They might spread rumors about her or use their popularity to make her an outcast. Another could be them using their supernatural abilities to intimidate her, like Edward using his mind - reading to embarrass her in front of others.
She might start by giving them the silent treatment. Just ignoring them completely when they try to talk to her, which would be a very human way of showing anger.
Well, it could be due to the way the Cullens interact with the other people in Forks. If Bella notices that they are being manipulative or using their powers in a way that she doesn't like to influence the townspeople, that could make her start to hate them. Also, if there is some kind of power struggle within the Cullen family that starts to affect Bella negatively, like she gets caught in the middle of it or she sees how it's causing harm to those she cares about, she might turn against them.
It could be another vampire clan. Maybe they are jealous of the Cullens' interest in Bella or they think that Bella's presence among the Cullens will disrupt the balance of power among vampires. So they try to get Bella from the Cullens, making them the main antagonists.
It could be that the fanfiction writer took a different approach to the story. In some fanfictions, the Cullens could be involved in situations that go against what Bella stands for. Perhaps they are written to be more secretive and untrustworthy, leading to Bella's hatred.
I'm not sure specifically as there could be many different takes on it. Generally, it might be about Bella using her singing in a context related to the Cullen family in a fan - created story.
Yes, it is quite common. Fanfiction writers often use this scenario to explore the relationship between Bella and the Cullens. It gives an opportunity to show the Cullens' caring side towards Bella.
In some fanfictions, the Cullens might hate Bella because of jealousy. Maybe other vampires are jealous of the attention she gets from Edward. Another reason could be that she brings too much danger to their family. Her presence could attract unwanted attention from other vampires or vampire hunters, which puts the Cullens at risk.
Her father, Charlie, might try to rescue her. He loves Bella deeply and would be very worried when she goes missing. He could start investigating and find out that the Cullens are involved.