In particular, I'm curious about two fights - the initial fight against the Dummy that Toriel has you fight, and the first encounter with Napstablook.
To stay on track for this route, do I need to kill Napstablook...
Well, sort of - do I need to deplete his health? He can't actually be killed, rather you deplete his health and he leaves.
...and the dummy, or can I mercy these two for speedrun purposes?