Hi Kevin. Both active and passive forms are fine here.

In truth, all of the sentences are passive in the sense that none states who plays the movie. Although #3 and #4 are the only actual examples of what would normally be termed "passive voice", any sentence that does not have a subject acting through a verb has passive characteristics. "Playing" and "showing" act as adjectives, not verbs, in #1 and #2. You can rewrite #1 in ways that make this more obvious: "Playing nationwide, this movie tells a story about a fox". (verb = "tells") "This movie, playing nationwide, tells an interesting story". (verb = "tells") "The currently playing movie is nationwide". (verb = "is") When you use the adjective "playing" to describe a movie you imply that the movie "plays". But, that action is only described. "Playing" is not an active verb, so it never ever has a subject even though it can describe the subject of a sentence. In the sentence, "The playing movie shocked the audience" the verb is clearly "shocked", not "playing". Here is a truly active sentence: "The movie now plays nationwide."

I'd use show or showing rather than play or playing and both are correct.

What about screen or screening?

Both forms are indeed correct and natural. As usual in choosing active or passive form, it depends on where the speaker/writer wants the attention (focus or emphasis) to be placed. In active form, the speaker wants the attention to be on the subject "the movie." In passive form, the speaker wants the attention to be on the action "being shown." Why choose active or passive? Well, passive may be preferred by those discussing scheduling or particular showings of the movie. Active may be preferred by those wanting to have a more dynamic tone perhaps in advertising the movie. So, an example could be in going to the movies with friends. Active form would most likely be used in talking about what movies are available. Passive form would most likely be used in talking about times of showing and location (perhaps in deciding which time is best). "Deadpool is showing this week." "Deadpool is being shown at Cinema A at 7pm."