I don't really see any correlation to a presentation on snake facts and Haruka's murder. The recommended list has several similar studies by other students. It is a big assumption to assume he has any kind of snake fetish, or that it is an unconcious metaphor. For all we know, his teacher gave them a subject, and told them what it needs to cover.
The motive for this is so unclear, but it seems to me she passed him while he was in the act of casing a van (this and what we know of his circumstances tells me he was desparate), and he saw an immediate opportunity to rob her. She fought back, it escalated, and he killed her. It is possible he also looked up and saw a beautiful girl, and thought, why not? And went after her to rape her. She fought back, it escalated, and he killed her. I do not think he had been stalking her or has been homicidal since childhood or premeditated the murder, though in those few seconds it is possible he thought she was a threat (looked at him weird, put her phone to her ear or pulled it out to make a call etc). If you try to get inside the mind of someone like this, they have absolutely nothing to lose - they are nonexistent, like shadows, and the longer they drift, the more shadowy they become. Life failed him and he took Haruka to pay it back IMO.