Connecting an actor’s onscreen personality with his or her offscreen reality tends to be a dicey proposition. But in “Faye,” an addictive and essential portrait of Faye Dunaway, it turns out to be the right thing to do. Dunaway, now in her early 80s, is interviewed throughout this HBO documentary, and there’s a knowing snap to her self-reflections that grabs you. Seated on a couch in her New York apartment, she starts off by chastising someone for bringing her water in a bottle instead of a glass — a sign that the movie is going to have fun with what a diva she is. As “Faye” presents it, Dunaway was too volcanic and troubled a personality not to pour herself into her roles. That’s part of what made her great. Yet the film also wants to cue us to the gossipy and reductive way that this kind of...