Maybe Sasuke teaches him the Chidori in a moment of camaraderie. And for the Rasengan, it could be an older and wiser Naruto from the future who travels back in time to teach his younger self.
I'm not entirely sure specifically as 'annabeth' is often from the Percy Jackson series and 'rasengan' is from Naruto. It could be a fan - created story that combines elements of both universes in some way, perhaps with Annabeth somehow getting involved with the power or concept of the Rasengan.
It's not based on a true story. The plot and characters were invented by the writers for entertainment purposes. There are no real-life equivalents or incidents that inspired it.
Definitely not. The vanishing of the sun is a concept usually found in science fiction or fantasy, not in reality. There are natural processes that govern the sun's existence and behavior, and vanishing is not one of them.