One possible motive could be that Snape is still deeply influenced by his loyalty to Voldemort in this fanfiction. Maybe Voldemort has some hold over him that forces him to do the unthinkable. Another reason could be a misunderstanding. Snape might believe that Harry has turned to the dark side or is about to, and he decides to take preemptive action to stop what he thinks will be a great evil.
Yes, it is a somewhat common theme in some fanfictions. One reason could be the complex relationship between Harry and Snape in the original series. Snape was often cruel to Harry, so in some alternate universes, writers explore the extreme scenario of Harry killing Snape. It also allows for exploring darker aspects of Harry's character and the consequences of such an act within the wizarding world.
One possible motive could be a misunderstanding. Maybe Snape is framed for something really bad, like a dark magic plot against Hogwarts. Harry, in his haste to protect the school and his friends, believes Snape is guilty and takes drastic action. Another reason could be if Snape accidentally endangers someone Harry loves dearly, like Ginny or Ron, and Harry's emotions get the better of him in the heat of the moment.
Perhaps in the fanfic, Snape discovers a powerful and dangerous magic that he wants to use for what he believes is the greater good, but Harry sees it as a threat. Harry has always been wary of Snape, and this new discovery could be the tipping point. Also, if Snape were to make a deal with a dark force in order to gain knowledge to defeat Voldemort but Harry misinterprets his intentions, it could lead to Harry killing Snape.
The 'Snape kills Harry' fanfiction would shatter the relationships that were built in the original series. For example, the friendship between Harry, Ron, and Hermione would be left in tatters. Hermione and Ron would be devastated and likely seek revenge. Also, Dumbledore's plan, whatever it was that involved Harry, would be completely ruined. The whole balance of good and evil in the wizarding world would be thrown into chaos.
In the original 'Harry Potter' series, the relationship between Harry and Snape was one of mutual dislike but also a certain level of respect in the end. However, in this fanfiction, it's a complete break. The fanfiction might change the power dynamics at Hogwarts as well. Snape was a key figure in the school's hierarchy, and his death at Harry's hands would send shockwaves through the staff and students, unlike anything in the original story where his death was a heroic sacrifice.
Well, in this kind of fanfiction, it might be that the writer wanted to subvert the typical relationship between Lily and Snape. Lily is often seen as a positive figure in relation to Snape. But if she kills him, it could be part of a story where the power dynamics or the moral compass in the Harry Potter universe is flipped. For example, if Lily was influenced by dark magic or some external force that made her see Snape as an enemy when he might not be in the original context.
One possible motive could be a severe misunderstanding. Maybe Harry is tricked into believing that Snape and Moody are involved in some dark plot against him or his friends. For example, if there were false evidence planted that made it seem like they were working for Voldemort again. Another reason could be that he was under the influence of a powerful dark magic that clouded his judgment and made him act out of character.
The reaction would also depend on how the events leading up to these actions were presented in the fanfiction. If it was made clear that Harry was acting in self - defense or to protect the wizarding world from a hidden threat, some might come to his side. But overall, it would create a huge upheaval in the wizarding world. The Ministry of Magic would be under pressure to take action, and there would be a lot of unrest among the students at Hogwarts who looked up to both Snape and Moody in different ways.
One plot could be that Snape is discovered to be working on a new dark magic spell that would endanger the whole wizarding world, and Harry, in an attempt to stop him, ends up killing him. Another could be a case of misinformation. For example, Harry is tricked into believing that Snape killed someone he loves dearly, like Ginny, and in his rage, he kills Snape before finding out the truth.