From the article:
When we went to our seats, the wait staff let us know that despite the fact that the previews were playing, we wouldn’t know until the movie actually started whether we could see the film or not. If it didn’t work, the screen would just turn black. Luckily, the film went through without a hitch.
Yes, the amount of showings that a theater has is tracked. Certain movies are contractually obligated to show at certain times or a certain number of times a day.