Characters could potentially be angry if they watch Hunger Games fanfiction. Imagine if a character has fought hard to be seen as a hero in the original story, but in the fanfiction, they are depicted as a coward. Their identity and the effort they put into their actions in the original story are being undermined. But on the other hand, some characters might take it with a grain of salt and just view it as an oddity of the fans' imagination, not getting too worked up about it.
It's a bit of a tricky question. On one hand, characters are fictional, so in a sense, they don't really have 'rights' in the traditional way. But if we think about them as having a certain essence or integrity, then yes, they could be angry. For instance, if a fanfiction changes the core values or relationships of a character in a way that goes against what the original story was trying to convey, that character could feel violated. However, some characters might be more open - minded and see the fanfiction as just another form of creativity, even if it's not entirely accurate.
Yes, they might. If the fanfiction distorts their character or does something disrespectful to their story, they could be angry. For example, if a character is made out to be a villain when they're not in the original story.