Some gods would be envious. Aphrodite might be jealous of the attention Percy gets because of this new and strange relationship. She could try to use her powers of love and charm to either bring Percy closer to her or to create more drama. Dionysus, on the other hand, would probably just be annoyed. He doesn't like getting involved in demigod drama most of the time, but this new situation would likely disrupt the order at Camp Half - Blood which he is supposed to oversee, so he'd be grumpy about it.
Most of the gods would be confused at first. Hera might see it as an opportunity to manipulate the situation for her own ends. She could try to use Percy's new connection to Ares to create more chaos or to further her own plans. Poseidon would be very conflicted. On one hand, he has a connection to Percy as his son, but now Percy has this new link to Ares which could put Poseidon in a difficult position among the other gods.
Well, some past gods might be amused. They'd see these modern interpretations of their stories and characters in the Percy Jackson fanfiction as a strange yet interesting new form of worship or at least attention. For example, Zeus might be a bit irked at some of the liberties taken with his character, but also secretly flattered that people are still so interested in him.
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.
Apollo would probably love it. Since he is the god of poetry and creativity, he'd be intrigued by the different interpretations of himself in fanfiction. He might even get some new inspiration for his own creative works from it.
The teachers at the school would be completely clueless. They'd be trying to regain control of the assembly, but when faced with gods, their normal disciplinary methods would be useless. One teacher might try to be brave and tell the gods to leave, only to be turned into a small, squeaking mouse by Hecate as a warning. Meanwhile, Percy and his friends would be scrambling to fix the mess before things got even worse.
Well, it could be about Percy discovering he has this unexpected connection to Ares. And then he has to deal with the reactions of his friends like Annabeth. Some of them might be distrustful of this new relation. Percy would then try to find out more about his connection to Ares through exploring old prophecies and ancient sites, all while trying to keep his regular demigod duties in check.
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.
In fanfiction, the relationship could be developed by exploring their family ties. Since Percy is a demigod and Ares is a god, there could be some underlying connection through the divine family tree. Maybe they discover that they are related in a more distant way than they thought. This could lead to Ares having a more protective side towards Percy, or Percy seeing Ares in a less antagonistic light. Also, they could be forced into a situation where they have to communicate their feelings and motives clearly, like being trapped in a magical prison together. This would make them open up and start to build a more complex relationship.
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.