One possible theme could be moral ambiguity. If Bella Swan is a criminal, it challenges the traditional view of her as a somewhat innocent character. It might explore how she got involved in criminal activities, like maybe she was pushed to it by circumstances in the fanfiction world.
Well, a frequent theme is the relationship building. How Bella forms relationships with the members of the BAU. Some fanfictions might focus on a romantic relationship between Bella and one of the agents, while others could be more about platonic friendships. Also, there's the theme of mystery. Since 'Criminal Minds' is all about solving mysteries, fanfictions might combine Bella's own mysterious side (due to her connection to the supernatural in 'Twilight') with the criminal cases the BAU has to solve.
Well, one possible plot could be that Bella's sister gets involved in some illegal activities in the vampire - human world of Twilight. Maybe she's stealing vampire artifacts to sell on the black market. And Bella has to decide whether to turn her sister in or help her cover it up to protect their family's reputation.
Power could be a motive. She might want to have control over the vampire world or the humans in Forks. So she starts doing villainous things to gain that power.
One great alternative theme could be 'Bella Swan and the Mysterious Newcomer'. This can create a story full of mystery and intrigue as Bella interacts with a new character in her town. It gives room for character development, relationship building, and a plot that can be both exciting and positive, far from the negative connotations of the original title.
Maybe she teams up with other characters who are also on the wrong side of the law. Together, they plan heists or other illegal activities. This would introduce new dynamics and relationships not seen in the original story.
One possible plot could be that Bella discovers she has a hidden talent for singing and uses it to win over Edward. Maybe she sings a song that reveals her true feelings for him in a way she couldn't express with words before.
One possible storyline could be that Bella discovers her Winchester heritage and has to learn how to hunt supernatural creatures like the rest of the family. She might struggle at first, but with the help of Sam and Dean, she becomes a skilled hunter.
A really interesting storyline could be Bella trying to reconcile her old life in Forks with her new life as a Mikaelson. She might struggle with the differences in values and lifestyles. For example, the Mikaelsons are more into power plays and manipulation in the supernatural world, while Bella was used to the more straightforward (although still complex) relationships in 'Twilight'. This internal conflict could be a major part of the story, along with her trying to find her place within the Mikaelson family and the wider supernatural community.
One common theme is 'alternate universes'. Writers often explore what would happen if Bella made different choices or if the Twilight world had different rules. Another theme is 'power discovery'. Many fanfictions focus on Bella finding new powers or abilities she didn't have in the original story. 'Love triangles' are also common, where Bella may be caught between different characters in new and interesting ways.
Yes, there are. You can find some on fanfiction.net. There are stories that blend the mysterious and romantic elements from both 'Twilight' (Bella Swan's origin) and 'Criminal Minds'. Some fanfictions might focus on Bella Swan joining the BAU in a unique scenario, bringing her own brand of tenacity and the special allure from the 'Twilight' world into the criminal - profiling realm of 'Criminal Minds'.