When Remus catches Harry cutting in the fanfic, his reaction would be one of immediate action. He would try to stanch any bleeding if there was any. He'd be very gentle but firm, telling Harry that this isn't the way to deal with problems. He'd then stay by Harry's side, listening to him, and trying to get Harry to understand that he's not alone and there are better ways to cope with whatever is bothering him.
Remus would be horrified. He'd probably quickly take the cutting tool away from Harry.
In a fanfic scenario, if Remus catches Harry cutting, he would likely be very concerned. Remus is a caring character. He might immediately try to stop Harry and find out what's wrong. He could use his calm and understanding nature to get Harry to open up about his troubles.
Sirius would be deeply affected. He'd see Harry as a sort of surrogate family, and seeing Harry in such a state would make him feel like he failed in protecting him. He'd do everything he could to make Harry feel better, from getting him medical help to just sitting and talking with him for hours about what's wrong.
Ron would probably be shocked. He always looks up to Hermione as the one who follows the rules. He might try to defend her at first, but then realize she was in the wrong. Harry, on the other hand, would be more understanding. He knows that sometimes there are more important things than just following the rules blindly.
Well, in that situation, Sirius would be shocked and heartbroken. He might first scold Harry for doing something so dangerous to himself. Then, being the impulsive person he can be, Sirius would probably take Harry to see someone he trusts, like Dumbledore or Madam Pomfrey. He would not let Harry out of his sight until he was sure Harry was okay and not likely to do it again.
He might use his Patronus. His Patronus could guide Harry out of a dangerous place or ward off Dementors that were about to attack Harry.
Well, at first, Harry could be alarmed. He has a protective nature, especially when it comes to Albus. If he catches them in a situation where they seem to be in over their heads, he might immediately step in to rescue them if necessary. He would then likely express his disappointment in their actions. However, if he realizes that their intentions were good, like trying to help a fellow student who was being bullied by using some unorthodox magic, he might be more understanding. He could guide them on how to use their skills and ideas in a more proper and approved way at Hogwarts.
He's probably furious. Snape has high standards for student behavior, and smoking is definitely not acceptable in Hogwarts. His face might turn red with anger, and his eyes would narrow as he glares at Harry.
She might get detention. Snape is strict, and cutting class is a serious offense in Hogwarts. He could assign her to clean the potions classroom or help with sorting ingredients in the dungeon.
He could also be secretly amused. Despite his stern exterior, Snape might see a bit of his own unrequited love in their relationship. So, he might give them a stern warning but not be as severe as he usually is.
One common theme is mentorship. Remus often acts as a mentor to Harry, guiding him in his magical studies and in understanding the wizarding world better. For example, in many fanfics, Remus teaches Harry about advanced defensive magic.