One reason could be betrayal. If someone he trusted, like a fellow ninja or an old acquaintance, turned out to be working for his enemies, that would surely make him pissed. It's a huge blow to his trust, which is a big part of his character.
Sasuke could be a possible cause. If Sasuke were to go back on his word about protecting the village or if he were to harm their friends again, Naruto would be pissed. Their relationship is complex, and Sasuke's actions often have a strong impact on Naruto.
Sasuke could make Naruto pissed off if he goes back to his old ways of seeking power and revenge. Naruto has worked hard to bring Sasuke back to the right path, and if Sasuke strays again, it would surely anger Naruto.
Yes, you are usually allowed to write 'pissed' in a short story. However, it depends on the context and the target audience. If the story is for a general or adult audience, it's more likely to be acceptable as 'pissed' is a common, if somewhat informal, way to say angry. But if it's for a very young or conservative audience, you might want to consider using a more mild term.
A new, powerful and arrogant villain introduced in the fanfic could be the cause. This villain could constantly mock Naruto and his ideals, and try to undermine his efforts to protect the village. Such blatant disrespect would make Naruto really pissed off as he is very protective of his home and the values he stands for.
Sasuke could be the cause. If Sasuke were to betray Naruto again in the fanfiction, it would surely make Naruto pissed off. Their relationship is complex and Sasuke's actions have a big impact on Naruto.
No, these are not common. People usually try to maintain their dignity and privacy, and such situations are not things that are regularly talked about in general society. It involves personal privacy and bodily functions which are not topics for normal public conversation.
The title 'peter parjer is pissed fanfiction' gives us some clues. 'Peter Parjer' is the name of someone, perhaps a character from a book, movie, or game that the fanfiction is based on. 'Is pissed' is an informal way of saying he's angry. Fanfiction can cover a wide range of genres and themes. So this could be an action - packed story where Peter's anger leads him into battles, or it could be a more emotional piece where he's pissed at a loved one and has to deal with the fallout. It could also be a comical take on his anger, with humorous situations arising from his pissed - off state.
I don't have information about the author of this particular fanfiction. There are so many fanfiction writers out there, and without more context or research, it's impossible to say who created it.