Percy would likely be very critical of their lifestyle. He comes from a world where family is important and they support each other in the face of danger. The Dursleys, on the other hand, seem to shun anything out of the ordinary and are unkind to Harry. Percy might try to show them a different way of living, with more love and acceptance, though they probably wouldn't listen.
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.
Percy would be completely devastated. He might go into a state of shock at first, unable to believe that Annabeth is really gone. Then he could become filled with rage, vowing to take revenge on whoever or whatever was responsible for her death.
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.
Percy would probably be cautious. He's been through a lot with the Greek gods, and he knows how powerful divine beings can be. So, he'd approach this new encounter with wariness.
The gods in the Percy Jackson universe would have mixed reactions. Some might see the daughter as a potential threat or a powerful ally. Zeus might be initially suspicious, but if the daughter proves her worth, he could be an important figure in her story. Poseidon would be proud, as he was of Percy. In the Naruto world, the village elders would be cautious. They would want to make sure the daughter uses her powers for the good of the village. But characters like Iruka would be very supportive from the start, seeing the potential for great things in the daughter.
Percy would most likely be extremely confused and frustrated. He has been through a lot already in his life as a demigod. Being forced into a marriage with Hestia would seem like another huge and unwanted burden. He may initially feel powerless against the will of the gods, but then his determination would surface. He'd start looking for ways to either change the situation or at least make the best of it while still maintaining his own identity and relationships with his friends.
Athena, being the goddess of wisdom, might analyze the fanfiction. She could look at how the mortal writers understand the Greek mythology and use it to create new stories. She might be impressed by the intelligence and creativity of some of the fanfictions, or she might be critical of inaccuracies.
Annabeth would probably be the first to try to calm Percy down. She's always been the rational one. She might use her knowledge of architecture and engineering to quickly assess the damage and come up with a plan to protect people. Grover, on the other hand, would be more worried about the nature spirits affected by the earthquake. He'd try to communicate with them to see if they can help in any way.
Elsa would probably be cautious at first. She has her own kingdom to protect and a stranger with unknown powers like Percy might seem like a potential threat. Anna, on the other hand, would be more curious and friendly. She'd likely want to know all about Percy and his world right away. Kristoff might be a bit skeptical, but he'd also be interested in seeing what Percy can do.