Yes, a recurring character knowingly puts themself in a dangerous situation to go after the killer and make sure they're dead so they can't harm the others anymore. They end up dying because of this.
Sort of. At a house party, some characters watch the original scream movie, and there are tons of meta references to the “stab” movies, which are the in-universe version of the scream movies.
No, though there is a scene where a car's headlights switch on and the engine revs seemingly by itself, which looks as though it's about to be driven into a character. It doesn't happen.
I feel like he counts.