In most cases, no. Reading fanfiction is generally not a criminal offense. Fanfiction is a form of creative writing by fans based on existing works, and simply reading it is like reading any other story. However, if the fanfiction involves illegal content such as copyright infringement on a large scale (but this usually pertains more to the writer than the reader), or if it contains illegal and harmful materials like extreme violence or illegal forms of pornography, there could potentially be issues. But for normal, non - offensive fanfiction, reading it will not land you in jail.
It could be that the Rogue Avengers in the fanfiction are withholding important information from Fury. He's a man who likes to be in control and have all the facts. If they're keeping secrets that could impact the overall situation, whether it's about a new threat or a powerful weapon, Fury would be justifiably mad.
Another theme is betrayal. Since they are 'rogue', the fanfictions may play up the aspect of them betraying the trust of their fellow Avengers. It could be about how their decisions to go against the main group led to a breakdown in relationships and alliances within the superhero community.
In such a fanfiction, the Rogue Avengers might initially be suspicious of Peter. They could test his loyalty and skills. Maybe Peter has to prove himself worthy to join their cause against the establishment Avengers. For example, he could show off his spider - powers in a unique way that impresses them.
One common theme is trust. Peter has to decide whether he can trust the rogue avengers, and vice versa. Another is the idea of family. The rogue avengers might see Peter as a new addition to their makeshift family. Also, there's often the theme of redemption, where the rogue avengers are trying to make up for their past actions through their interactions with Peter.
The interactions would likely start with suspicion. The rogue avengers, having been through a lot, would be cautious. Peter, though, would be eager to connect. He might start by trying to help them in some small way. As they interact more, the rogue avengers could see Peter's potential and Peter could learn from their experiences. There could be moments of humor, like Peter making a joke that lightens the mood, and also serious discussions about their different views on heroism.
One possible plotline could be the process of how the rogue Avengers are pardoned. Maybe they have to complete a series of dangerous missions to prove their loyalty again. Another could be the internal conflicts within the group as they adjust to being pardoned and reintegrated into society.
It could be Hydra. They might be trying to take advantage of the split between the Avengers and the Rogue Avengers. They see Peter as a wild card and try to either capture or turn him against both groups.
In this fanfiction, Peter Parker might initially be in awe of the Rogue Avengers. He could try to prove himself to them, showing off his Spidey skills. Maybe they start off distrusting him, seeing him as just a kid, but as they face challenges together, they come to respect his abilities and his big heart.