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.
A fanfiction could revolve around Captain Marvel losing her powers temporarily and Nick Fury having to protect her while also trying to find a way to get her powers back. This would put their relationship to the test and show how much they rely on each other in different ways.
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.
Their personalities can clash because Captain Marvel is a powerful and independent hero. She might not always want to follow Nick Fury's orders. For example, she could be more impulsive in a fight, while Fury is all about calculated moves. But they can blend as the story progresses. Maybe after a big argument where Captain Marvel's impulsive move almost gets them in trouble, she realizes Fury's wisdom. And Fury, in turn, sees her courage and determination and starts to respect her more independent style.