I'm not sure specifically which 'the black monkey story' you are referring to. There could be many stories involving black monkeys in different cultures or fictional works.
One common scenario in such fanfiction could be that Black Cat is jealous of Spiderman's secret identity. She might feel like she doesn't really know the whole of him. This could lead to her trying to find out more about Peter Parker, which could cause all sorts of problems. For instance, her investigations might draw the attention of Spiderman's enemies who are also interested in his true identity.
It's very likely that such a fanfiction exists. Fanfiction is a vast and diverse world where writers can let their imaginations run wild. Since Black Cat has her own motives and character traits, and Spiderman has his enemies and challenges, a scenario where Black Cat kills Spiderman could be an interesting exploration of betrayal, revenge, or a change in the status quo. There may be multiple versions of such a fanfiction, each with different interpretations and story developments.
I'm not sure specifically as there could be various 'black ops monkey stories'. It might be about a monkey involved in some sort of covert or special operations, perhaps in a fictional or very specific military - like scenario.
Yes, it is quite a popular trope. The relationship between Spiderman and Black Cat has always been complex and full of intrigue in the comics. Their interactions, including a kiss, add a layer of romance and drama to the stories. Many fans are drawn to this aspect as it shows a different side of Spiderman's character, one that is involved in a more passionate and somewhat dangerous relationship compared to his more well - known relationship with Mary Jane.