It could be a rogue member of the Order. Maybe someone who has their own agenda and decides that Harry is a threat to their plans. So they manipulate the Order into kidnapping Harry, but then they have their own evil intentions for him.
In this fanfiction, perhaps Harry is kidnapped by the Order because they think he's being influenced by dark forces. As the story unfolds, he could start to understand their reasons while also uncovering a traitor within the Order who wants to harm him for real. Or, he might use his skills to turn the situation around and make the Order see that they were wrong to kidnap him in the first place. He could then lead them in a new direction against Voldemort.
There may be. Fanfiction writers come up with all sorts of creative scenarios. However, the popularity of a 'Harry Kidnapped' fanfiction might vary. Some might be really well - written with complex plots and character development, while others could be more simplistic. It really depends on the writer and what they're trying to convey with the kidnapping concept.
One possible fanfiction could involve a complex plot where Olivia is kidnapped by a criminal she once put away who has escaped from prison and is seeking revenge. His minions manage to ambush her when she's off - duty, perhaps near her home. Her team then has to race against time to find her, using their skills and knowledge of past cases to track down the kidnapper.
One possible fanfiction could be that Harry Potter is kidnapped by a dark wizard who has some strange power that makes Harry squint. Maybe this wizard is trying to use Harry's unique connection to Voldemort for some dark ritual. Harry has to use his wits and the few spells he can manage while squinting to try and escape.
Perhaps Olivia is kidnapped by a group of human traffickers. They mistake her for an easy target, not realizing she's a detective. The fanfiction could detail her experience in the hands of the traffickers, how she tries to resist and escape, and how the SVU team uses their resources and connections to track down the traffickers and rescue her.
Another reason could be that Harry sees the Order as being too cautious or old - fashioned in their approach to fighting Voldemort. He might believe that their traditional methods are not enough to defeat Voldemort quickly and effectively, and this lack of progress makes him angry at them.
Maybe he feels that the Order is keeping secrets from him. In many fanfictions, Harry can be a character who values honesty and when he discovers that the Order, which he may consider an ally, is hiding things from him, it can make him angry.
At the beginning, Harry would be frightened. He's in an unknown place with Loki, who is known for his trickery. But Harry is no pushover. He would quickly gather his courage. He would remember all the times he's faced danger at Hogwarts. He might try to communicate with Loki to understand his motives. If Loki reveals that he wants to use Harry's magic for something, Harry would try to find a way to outsmart Loki. He could pretend to cooperate while actually looking for a weakness in Loki's plan. Harry would also be thinking about his friends at Hogwarts and how he needs to get back to them, which would give him extra motivation to fight back against Loki.
Harry might initially be very confused. He trusts Albus to some extent, so he would be bewildered as to why this is happening. He could try to reason with Albus at first.