Well, one possible plot development could be that his friends start a rescue mission right away. They might use magic to track the vampire's lair. For example, Hermione could use her extensive knowledge of spells to create a tracking charm. Another development could be that Harry discovers some hidden power within himself while being held captive, something that he can use to either escape or fight the vampire when the time comes. Maybe he has some latent ability related to his connection with Voldemort that can be used against the vampire's dark magic.
His best friends, Ron and Hermione, are most likely to come to his rescue. They've been through so much together and would never abandon Harry. Ron would bring his loyalty and courage, while Hermione would use her brains and magic skills. Also, Dumbledore or other powerful wizards from Hogwarts could step in. Dumbledore, with his great wisdom and powerful magic, would surely not let Harry be in the hands of a vampire for long.
Not really. Fanfic writers usually create stories that are more in line with the positive image of Harry Styles. They might write about meeting him backstage, going on a date with him, or being friends with him. A 'Kidnapped by Harry Styles fanfic' goes against the norm as it involves a rather negative and dangerous situation, so it's not a common type.
I'm not entirely sure as 'fanfic' can vary greatly. It could be about Harry Potter being kidnapped in some alternate storyline created by a fan. Maybe it's a dark plot where Voldemort or some new villain has abducted Harry for their own evil purposes.
There's a good chance. Fanfics are known for their creativity and bending of established norms. If the fanfic is centered around this idea, then Harry could very well be an ancient vampire. This could lead to interesting plotlines involving his vampiric powers, his interactions with other characters who may or may not know his true nature, and his struggle with his new identity.
Well, perhaps in the fanfic, the kidnapped character is a rival in love for Harry Styles in the eyes of the kidnapper. The kidnapper might be so obsessed with Harry that they see anyone getting close to him as a threat, so they kidnap this person. They could hold the kidnapped person in a secret location and try to make them stay away from Harry Styles.
Well, it could be that Harry is under the influence of a dark spell which makes him kidnap Parvati. Then perhaps his friends, like Hermione and Ron, have to find a way to break the spell and rescue Parvati while also trying to understand why Harry did this in the first place.
You can try looking on some popular fanfic websites like Archive of Our Own (AO3). There are a lot of Harry Potter fanfics there, and you might be able to find ones related to this topic by using the search function.
He'd probably be really confused at first. I mean, he's used to the world of magic and suddenly he's faced with these superheroes from a completely different realm. He might try to use his magic to escape, but if he realizes they're not necessarily bad guys, he could start to negotiate with them.
It could be Voldemort or one of his Death Eaters. They might be using Harry as a pawn to get to Parvati for some reason, like she has a special power or knowledge that they want.