The Movie Drive, A Question About the Elevator Scene (Spoilers)

How does the hit man know it's them? After the "hero" sloshes the babe's throat with his tongue, an item I also assume he never even motorboats, it appears like the assassin makes the first move to kill.

How does the guy know it's him? Did I miss something? Was he in another scene and saw him somewhere? Are we just to assume that, or does the guy just kill random people because that's what he does?

This may have been asked before, I put spoilers in it, but I'm probably about the last person to see this movie.

And the ending was okay I guess, but shouldn't he have donned the fake face for that scene and gone in and somehow messed him up in the restaurant with some sort of surprise ending, instead of using it in the cliff scene? He really didn't even need it for that scene. Fake face in the last seen, that would have been more entertaining to me. And they could have thought of some way to make him still look like the defensive good guy.