Another way Harry can outwit Snape in fanfiction is through his relationships with other characters. He might enlist the help of Dumbledore, who could give him some advice or a plan to deal with Snape's suspicions. Or he could work with Hermione and Ron to create a diversion or a clever scheme. For instance, they could stage a fake emergency in one part of the castle while Harry slips away to do something important that Snape has been trying to prevent.
Harry could also outwit Snape by using his quick thinking and ability to improvise. Suppose there is a situation where Snape is trying to catch Harry doing something wrong. Harry might use the chaos around him, like a commotion caused by other students, to his advantage. He could blend in with the situation, making it seem like he's innocent while actually achieving his own goals, like getting access to a restricted area for a noble reason that Snape doesn't initially understand.
In some fanfictions, Snape might use his advanced knowledge of potions to create a special concoction to heal Harry. He could draw on his skills in Herbology as well to find rare ingredients for the potion.
As the story progresses, they might start to work together more closely. Snape could be teaching Harry some advanced magic that no one else knows, and through this process, they build a bond. Harry begins to understand Snape's past better and realizes that they have more in common than he thought, like their love for Lily Potter in different ways.
In this kind of fanfiction, Harry often becomes more proficient in potions and other areas that Snape is good at. His relationship with Snape also makes him more empathetic towards Snape's past and the Slytherin house in general. He may not be as quick to judge people based on their house. Also, he might develop a more complex view of the wizarding world's politics, as Snape is deeply involved in some of the darker aspects of it.
In some fanfictions, yes. Writers often explore the complex relationship between Harry and Snape. They might create scenarios where Harry discovers Snape's true loyalties and motives earlier than in the original books, leading to a new level of trust.
In some fanfictions, Snape might rescue Harry Potter by using his knowledge of the Dark Arts to counter a dark spell aimed at Harry. For example, if Voldemort or his Death Eaters were about to cast a fatal curse on Harry, Snape could step in and deflect it with a powerful counter - curse. He is a very skilled wizard, after all.
Snape's character often develops from a cold and aloof figure to a more caring and father - like one. He starts to see Harry not just as James Potter's son but as an individual he is responsible for. His protective instincts grow, and he becomes more patient. For example, he might initially snap at Harry for small mistakes but over time, he learns to guide him gently.
In some fanfictions, Snape might share some of his knowledge about the wizarding world's secrets with Harry. Maybe he tells Harry about certain spells or magical artifacts that could help Harry in his fight against Voldemort. This act of sharing knowledge is a way of being nice as it gives Harry an advantage in his battles.
Harry in this fanfiction might be a lot more complex. His identity is no longer that of the Boy Who Lived in the traditional sense. He has to come to terms with the fact that his parents are two very different and controversial figures. He may become more of an outcast, even among his friends at Hogwarts. His sense of right and wrong could be more blurred, as he has the influence of Bellatrix's dark ways and Snape's own morally ambiguous actions. He might be constantly questioning his own nature and whether he is destined to follow a path of good or evil.
Perhaps in this fanfiction, Snape has proven himself to Harry in some extraordinary way. Maybe he has saved Harry's life multiple times or has shown his true loyalties that were hidden in the original story. It could also be that Snape has some special connection with Harry that makes Harry trust him unconditionally.
Harry might start by making a list of all the wrongs Snape has done to him over the years. This would include things like unfair grading, public humiliation, and general nastiness. Then, he could look for ways to expose these actions to the rest of the wizarding world. Maybe he would use the wizarding newspapers or even start his own blog (if there were such a thing in the wizarding world) to share his experiences. He could also try to find allies among the students and faculty who have also had problems with Snape.