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?

2 Answers

No. Neither the dummy nor Napstablook count. It is faster to use Act->Talk on the dummy, and to grind all encounters in the three rock room before Napstablook: if you have already exhausted the encounters in RUINS by the time you meet Napstablook, he will simply fade away.

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you can just spare those two. fighting napstablook actually gets you negative EXP, as well as taking time, so he's better avoided.

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