In the fanfiction, Snape could protect Harry from Dumbledore by using his skills in potions. For example, he might create a potion that hides Harry's magical signature from Dumbledore's detection. Or he could use his knowledge of the Dark Arts to counter any spells or charms that Dumbledore might use to keep tabs on Harry. Snape is very intelligent and resourceful, so he could find various ways to physically and magically shield Harry from Dumbledore.
One reason could be that Snape has his own complex sense of loyalty. He may feel that Dumbledore's plans for Harry are too dangerous or not in Harry's best interest in some ways. He has a long - standing relationship with Harry's mother, Lily, and perhaps through that connection, he wants to safeguard Harry from any harm that might come from Dumbledore's actions or decisions.
Well, he might use his magic skills. Maybe he creates some protective spells around Harry to keep the werewolf at bay. For example, a strong shielding charm that can withstand the werewolf's attacks.
Well, perhaps one of the other teachers might have noticed Snape's behavior towards Harry and reported it to Dumbledore. It could also be that Dumbledore, being as perceptive as he is, noticed Snape's extra harsh treatment of Harry during their interactions in the corridors or in class.
In some fanfictions, there could be other dark wizards or witches who are allied with Voldemort or have their own reasons for wanting to harm Harry. Snape would have to protect Harry from these various threats as well. For example, some Death Eaters might try to take matters into their own hands and go after Harry without Voldemort's direct orders.
Typically, it portrays Dumbledore as a manipulator. He's seen as using Snape's feelings for Lily and Harry's role in the fight against Voldemort for his own purposes, rather than having pure intentions.
Dumbledore, as Harry's guardian in the fanfiction, would probably use his influence in the wizarding world. He could make sure that Harry is taught by the best teachers at Hogwarts. He'd also be there to offer advice and guidance, especially when Harry faces challenges like dealing with Voldemort or other dark forces. For example, he might teach Harry some advanced defensive magic privately to better protect himself.
Snape might be given a warning by Dumbledore at first. Just a simple 'stop this behavior or else' kind of warning.
In many such fanfictions, Dumbledore might comfort Snape by reminding him of his good deeds. For example, he could say that Snape's role as a double agent is crucial for the greater good. Dumbledore might also offer a sympathetic ear, listening to Snape's inner turmoil about his past actions and his love for Lily. By validating Snape's feelings and his importance in the fight against Voldemort, Dumbledore provides comfort.
Dumbledore can hurt Snape in fanfiction by taking advantage of his love for Lily. He might use this love as a tool to manipulate Snape into doing dangerous tasks. For example, making Snape spy on Voldemort, knowing full well that Snape's life is at risk every time he does so.
One common reason could be his love for Lily. Since Harry is Lily's son, Snape might feel an obligation to protect him out of his undying love for her. It's like he's trying to preserve a part of Lily that still exists in the world through Harry.