Well, usually in such a manga, the girl is held against her will, maybe in a secluded place. There could be attempts to rescue her by friends or heroes, and lots of tension and drama along the way.
There are few common elements that might be in such a story. If a girl kidnaps a boy, perhaps she has a hidden motive. It could be related to a family feud, where she believes the boy's family has wronged hers and she takes the extreme step of kidnapping him. Or it might be a case of a deranged love, where she is obsessed with the boy and wants to keep him all to herself by force.
It might be. True stories often get turned into books to raise awareness or share someone's harrowing experience. But one would need to research the background and author's claims to confirm its authenticity.
Perhaps the anime girl was kidnapped because she holds a special key or knowledge that the military guards want. She could be from a world where anime rules apply, and her knowledge of that world's magic or technology is what attracted the military's attention. She will then go through a series of adventures within the military compound, making friends with some of the inmates (if there are any) and planning her great escape.
Sure. There are stories out there. Some might be in the horror genre where a boy is kidnapped by some deranged person or group with a strange obsession about changing his gender. This could be used to create a sense of unease and to play with the idea of losing one's true self. However, these are often quite dark and disturbing concepts.
Start with a bang! You could describe the moment of the kidnapping vividly. For example, 'The anime boy was walking home from school, his head filled with thoughts of the day's events, when suddenly a black van screeched to a halt beside him. Before he could react, strong hands grabbed him and yanked him into the van.' This immediately grabs the reader's attention.
One plot idea could be that the anime boy is kidnapped by a group who wants to use his special powers for their own evil purposes. The fanfiction could then focus on his friends trying to rescue him. Another idea is that he's kidnapped due to a misunderstanding, like being mistaken for someone else who is actually a criminal. Or perhaps he's kidnapped by a fan who has an unhealthy obsession and the story could be about his struggle to escape and deal with this extreme situation.