"Do you often go to the movies?"
Translation:Käytkö sinä usein elokuvissa?
We don't really use "mennä" in this sense. "Käydä" is more natural way to say it. "Käydä" is used with short visits (such as the movies, restaurants, museums etc.) and regular visits that you do.
Here's a source about this where the difference is explained: http://randomfinnishlesson.blogspot.com/2017/02/the-difference-between-menna-and-kayda.html?m=1
I have always preferred "mennä" over "käydä" in cases like this. I agree that "käydä" is more natural for short visits, but here it really depends what you yourself think is a short visit. For example I always say "mennä elokuviin" (go see a movie) and "mennä pelaamaan golfia" (go play golf). I also always say "käydä kaupassa" (go to/visit the store). However, I would use "käydä" if I explicitly wanted to emphasize that I will be back soon, or that going there takes less time in relation to something else. For example "haluatko mennä ulkomaille vai käydä elokuvissa?"
About usage of "käydä" when talking about regular visits: that doesn't apply here. If the phrase was "Do you go to the movies regularly?" then I agree that the correct translation is "Käytkö säännöllisesti elokuvissa?"
My point is, "Menetkö (sinä) usein elokuviin?" should be accepted here.