Percy would probably be a bit wary at first. He's used to the demigod world and Fury's whole S.H.I.E.L.D. thing would seem really different. But Fury would be all business. He'd likely be sizing Percy up, trying to figure out how to best use his powers.
One common theme is adventure. Since Nick Fury is often involved in dangerous and high - stakes missions, the reader gets dragged into these adventures. Another theme is trust. The reader and Nick Fury have to build trust in each other in the face of various threats.
In the comics, Nick Fury is indeed shown as black. This portrayal has been consistent over time and is an important aspect of the character's representation.
Yes. Nick Fury is black in the comics. This has been a consistent part of his character design and has been maintained throughout various comic storylines and adaptations.
Yes, there are quite a few. You can start by looking on fanfiction.net or Archive of Our Own. Just search for 'Captain Marvel x Nick Fury' and you'll find a variety of stories with different themes, from action - packed adventures to more character - centric relationship - building ones.
One common theme is teamwork. Given their different skills, it's often about how they combine forces. Another is trust - building, as they come from different backgrounds in the Marvel world.
Perhaps in this fanfiction, the Olympians are concerned about the growing power of the superheroes. Percy is sent as a liaison to Nick Fury. Fury, initially skeptical, soon realizes Percy can be a great asset. Together, they work to maintain peace between the two very different worlds of demigods and superheroes.