Yeah, he is, but he's an artist first, fighter second, like we saw during this fight as well. Which is just fine, since that's his role and he's pulling it off well. A bard in RPG terms.
I counted that as finishing her off. The same as kicking her into the sea. That is, doing anything at all to make sure she wouldn't stand up and continue the fight.
My memory being what it is, I can't be absolutely sure, but I have quite a solid feeling Zoro has been called that before, in one way or another. At the very least the second in command if not vice captain literally.