His courage becomes more evident. By saving Hermione, he shows that he is willing to face great danger for his friend. This act of heroism can make him more confident in his abilities as a wizard.
Well, in many such fanfictions, Harry might use his magic skills. He could cast a powerful stupefy spell on the troll to stop it in its tracks and then quickly lead Hermione to safety. Maybe he also uses his quick thinking and knowledge of the Hogwarts corridors to find a hiding place where the troll can't reach them.
In this kind of fanfic, one possible scenario could be that Harry uses his quick thinking and magical skills. For example, he might use a stunning spell on the troll just in time to stop it from harming Hermione. Another scenario could be that Harry lures the troll away from Hermione, using his knowledge of the troll's behavior. Maybe he throws something noisy in the opposite direction to draw the troll's attention.
Hermione could develop a more complex understanding of magic. Since saving Harry's parents would likely involve delving into some very rare and powerful magic, she would expand her knowledge greatly. This new knowledge could make her more respected among the wizarding community, and she might use her new status to advocate for better magical education and research, all while her character grows in wisdom and leadership.
Harry might develop more patience. Usually, he can be a bit impulsive, but when it comes to saving Hedwig, he has to be careful. He has to think through his actions before making a move. For example, if he's facing a powerful dark wizard who has Hedwig captive, he can't just rush in. He has to plan, and this planning helps him grow as a more patient person.
Severus might start off as just fulfilling a sense of duty. He has always been a complex character. But as he saves Harry from the Dursleys, he begins to see Harry in a new light. He realizes that Harry is not just James Potter's son but an individual with his own struggles. This could lead to him becoming more empathetic towards Harry, gradually shedding some of his cold exterior.
Hermione might become more distrustful of Ron. After being saved by Lucius from Ron, she could start to see Ron in a different light, perhaps as someone with a darker side she hadn't fully recognized before. This could make her more cautious in her interactions with him.
Well, it could start with Hermione being in a vulnerable situation, like being cornered by the troll in a dark, damp dungeon. Harry, being the brave hero, arrives just in time. He might first distract the troll by conjuring up some annoying little creatures that the troll would start chasing. Then, when the troll's back is turned, Harry would grab Hermione and apparate them both to a safer place, like the Gryffindor common room.
Hermione's character could develop in terms of her relationships. Through saving Fred, she might form a stronger bond with the Weasley family. She may also become more empathetic as she experiences the fear of losing someone dear. She realizes that there are things more important than just academic knowledge. So, she starts to balance her intellectual side with her emotional side more effectively.
One reason could be that the troll is simply on a rampage and Hermione was in the wrong place at the wrong time. Trolls are not known for their intelligence, and it might have just stumbled upon Hermione while wandering the Hogwarts halls.
Maybe Harry uses his magic skills to immobilize Ron. He could cast a spell like 'Petrificus Totalus' on Ron right when he's about to attack Hermione, thus stopping the beating.