A villain like Shigaraki would likely be interested in the power levels in the MCU fanfiction. He's always looking for ways to increase his own power, and seeing the various powerful artifacts and abilities in the MCU might give him some ideas. He could think about how he could use similar things in his own plans to take over the MHA world.
Another fictional hawk could be 'Hawkeye' which is a name that can be associated with a hawk - like character. It gives the impression of a character with sharp vision and a focused, predatory nature, much like a real hawk.
She might be initially scared but quickly regain her composure. Uraraka is a brave character. She would likely start looking for ways to escape, using her zero - gravity quirk to her advantage, like floating up to vents or disabling the villains' weapons if she can.
Shigaraki would likely be disgusted if the fanfic made him seem weak or less of a threat. He'd probably scratch at his neck in irritation. Dabi would be dismissive. He'd think fanfics are just a waste of time and not worthy of his attention. Toga, though, might be intrigued. If the fanfic had a lot of blood and gore in it, or if it focused on her relationships in an interesting way, she could be really into it.
They might get angry if the fanfiction shows the heroes in a very positive light and the villains as weak or stupid. They have their pride and don't like to be made fun of or belittled, even in fan - made stories.
Izuku would probably be terrified at first. After all, he's been kidnapped by villains. But then, his hero - like determination would kick in. He might start looking for ways to escape or at least resist their plans.
For heroic - centric fanfictions, they would likely be disdainful. Since they oppose heroes, seeing stories that glorify heroes would annoy them. They might scoff at the idealized versions of heroes in those fanfictions.
The Hawks' back story could involve their origin as a sports team. They might have started in a particular city with a group of passionate players and investors. Maybe they were initially part of a smaller league and then grew to be in a major one. Their name could be inspired by the characteristics associated with hawks, like speed and precision.