One possible plot could be that Kol kidnaps Elena to use her as bait for his enemies. He might think that by having Elena in his custody, her friends, especially the Salvatores, would come to rescue her and he could then ambush them. Another idea is that Kol has some sort of vendetta against Elena because of her connection to the doppelganger bloodline. So he kidnaps her to extract revenge on the entire line.
The Salvatores, Damon and Stefan, are likely candidates. They have always been protective of Elena and would do anything to save her. They could use their vampire skills and knowledge of Kol's weaknesses to stage a rescue.
They could develop a shared hobby. For instance, they both get into painting and use it as a way to express their emotions and connect on a deeper level. It would be unique because it shows a side of them that's not related to their supernatural natures.
I'm not sure specifically as it depends on the particular fanfiction. It could be a story where a character named Kol kidnaps Bonnie within the universe of the show or book that the fanfiction is based on. Maybe it's part of a complex plot involving magic, power struggles, or personal vendettas.
She could be terrified at first. After all, Klaus is a very powerful and dangerous vampire. But Elena is also a strong - willed character. So she might quickly gather her courage and start looking for ways to escape.
The Salvatore brothers, Stefan and Damon, are the most likely candidates. They both have a strong connection to Elena and would stop at nothing to rescue her. Stefan's sense of chivalry and Damon's fierce protectiveness would drive them to track down Katherine and get Elena back.
Elena would likely be angry. She has her own agency and doesn't like being controlled. If Stefan kidnapped her, she would fight back. She might use her knowledge of the supernatural world and her relationships with other characters to try to escape. For example, she could try to call out to Damon telepathically if they have some sort of connection in the story.
In many 'The Vampire Diaries' Kol and Elena fanfictions, their relationship can be quite complex. Kol is often depicted as a wildcard, and his interactions with Elena can range from intense and dangerous to oddly alluring. Some fanfictions might explore a forbidden - love - type scenario, where Kol's vampiric nature and his family's history with Elena's friends create barriers. However, they also might find common ground in their mutual experiences of being caught up in the supernatural chaos of Mystic Falls.
The other vampire clans might be antagonists. They could see the baby as a threat to the vampire hierarchy or fear that the baby will have powers that could disrupt the balance among vampires. For example, the Originals' siblings who don't trust Kol might try to stop Elena from having the baby.