At first, Percy would be in shock. He'd be taken from his familiar world of demigods and suddenly be in this strange place with Dumbledore. But then his survival instincts would kick in. He'd start looking for weaknesses in his captor and the environment. He might try to reason with Dumbledore at first, but if that doesn't work, he'd resort to using his powers. He'd also be constantly thinking about how to get back to his friends and family at Camp Half - Blood, and he'd be worried about what threats they might be facing without him.
Percy would first be confused. He doesn't know Dumbledore or the wizarding world. Then he'd likely become defiant. He has a strong sense of loyalty to his friends and his own world, so he'd want to escape and get back. He might also be a bit curious about the new magic around him, but his main goal would be to get free.
Percy would be really angry. He's used to being in control of his own situation, and being kidnapped is not something he would take lightly. He'd probably try to fight back right away, using his demigod powers like his sword fighting skills and his ability to control water.
Well, in a fanfiction scenario, if Dumbledore kidnapped Percy Jackson, it could lead to a really strange and interesting mix of the two universes. Dumbledore might be interested in Percy's powers, especially his connection to the water and his demigod abilities. Maybe he wants to protect Percy from the threats in Percy's world by taking him to Hogwarts. But Percy would surely be confused and probably try to escape to get back to his friends and his own world.
Hermione would be extremely worried and would start researching like crazy to find out where Dumbledore has taken Harry. She would probably suspect that something is not right with Dumbledore and would try to convince Ron to help her. Ron, on the other hand, would be initially shocked but then would be ready to go on a rescue mission with Hermione.
At first, Harry would be in shock. He would be full of disbelief that Dumbledore, of all people, would do such a thing. He would struggle both physically and emotionally. Physically, he would try to break free from whatever bindings or magical restraints Dumbledore has put on him. Emotionally, he would be a mess, feeling hurt, scared, and confused. However, depending on how the story unfolds, he could gradually come to terms with the situation if Dumbledore manages to convince him that it's all for a greater good.
The Ministry of Magic would probably be in an uproar. They might see Dumbledore's actions as a blatant abuse of power. They would send out Aurors to search for Harry and arrest Dumbledore. After all, Dumbledore is one of the most powerful wizards, and his actions would be seen as a threat to the stability of the wizarding world.
The gods might also get involved. Zeus, for example, would not be happy that a human organization had kidnapped one of his son's (Poseidon's) demigod children. He might send some signs or even directly interfere. Athena would be giving Annabeth advice on how to deal with SHIELD. And Poseidon himself might stir up the seas near SHIELD facilities to show his displeasure.
The characters' reactions would vary widely. Annabeth would likely be critical of any fanfiction that got the details of her character or her knowledge wrong. She's very intelligent and detail - oriented, so inaccuracies would bother her. On the other hand, if a fanfiction captured her essence well, she might secretly enjoy it. Leo would probably be excited to see all the creative ideas people had in fanfiction, especially if there were cool new inventions or adventures in them.
Percy would also be determined. He's faced many tough situations before, and this would be no different. He'd draw on his inner strength and the support of his friends. He might feel guilty for not being able to protect his sister in the first place, which would fuel his determination even more to get her back.
Percy would feel a deep sense of guilt as well. He might think that he should have been there to protect her. So, he would be determined not only to free her but also to make sure whoever is responsible pays for what they've done. He would use his powers over water to his advantage, like creating distractions or using water to weaken the enemy's defenses while he tries to reach Annabeth.
Percy would probably be very confused at first. He's used to dealing with threats from the world of Greek mythology, not superheroes like the Avengers. But once he realizes he's been kidnapped, he'd likely be angry. He'd try to find a way to escape using his powers, like controlling water to create distractions or even using it to overpower his captors.
His first reaction might be shock. Dragons aren't exactly common in his world, even with all the mythical creatures. But then his hero instincts would kick in. He could try to befriend the dragon, thinking it could be an ally in future battles against the Titans or other enemies. He might offer it some food, like a fish or something, to gain its trust.