#1 is my favourite

Good point! The group we call moths is paraphyletic (meaning we can't make a group all of the moths and their common ancestor without including the butterflies). So yes, it is a butterfly, which means it's also a moth. It's like how, cladistically speaking, birds are reptiles and humans are fish.

Looks like a Skipper of some kind to me (family Hesperiidae), which are indeed butterflies