Annabeth would be devastated. She and Percy have a deep connection. She might go into a state of shock at first, then be filled with a fierce determination to find out who was responsible and make them pay. She would probably also be racked with guilt, thinking she could have done something to prevent it.
The other demigods at Camp Half - Blood would be in shock. Percy was a hero to many of them. Some would be angry, feeling that the gods should have protected him better. There would be a general sense of unease and fear, as if the safety net that Percy represented was now gone. They might also start to question their own fates more seriously.
Grover would be heartbroken. As Percy's best friend, he would mourn deeply. He might feel like he lost his protector as well as his friend. Grover would likely use his nature - related powers to create some sort of memorial for Percy, perhaps a grove of special trees that are said to hold the spirit of the fallen hero.
Grover would be panicked. He's Percy's friend and he cares a great deal about him. He might start running around trying to find help, like looking for a healer or someone with magical healing abilities. He'd probably be muttering to himself about how he should have protected Percy better.
They might be very skeptical at first. After all, Percy's powers are based on Greek mythology which is quite different from their world.
Annabeth would be completely devastated. She would probably go into a state of shock at first, then be filled with anger and determination to find a way to bring him back, if possible. She might even go on a solo quest to try and reverse his sacrifice.
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 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.
Grover would be really worried. He's always been Percy's protector in a way. He would be concerned about how this would affect Percy's life and safety. He might also try to help Percy find resources or support within the demigod community.
Some fans might be intrigued. They could see it as an interesting exploration of 'what if' scenarios, even if it goes against the grain of the original story. However, a large number of die - hard fans would probably be quite upset as it goes against the strong bond that was built up between the two characters throughout the books.
He'd probably be shocked. Percy is used to living his own story, not reading someone else's take on it.
Some of them might be entertained. For example, Thor could see the similarities and differences between his world and Percy's world of gods and monsters and find it humorous. Others like Black Widow might analyze the characters' motives and strategies in the fanfic as she is used to understanding people's minds.
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.