‘Film’ is an old technology. You would use it as a verb if you are talking about the past, or if you are taking about the world of commercial cinema. The series was filmed/shot in Slovenia. Let’s go see a film/movie. They made a film about Caesar. (Not ‘filmed a film’ which sounds a bit silly) Otherwise we’d use words like ‘shoot’, video’ or ‘take a video’. I also think ‘record’ is ok informally as short for ‘video-record’ as long as it’s obvious from context that it wasn’t only the sound. I recorded the game and will post it on YouTube. Can you take a video of the speech? I videoed all my kids’ events. The competition is shot remotely.

"Film a film" is not wrong, but it sounds weird. You can say "film a movie" or "make a film". We wouldn't say "record a film", but a long time ago in the age of VHS videotapes, we would say "I recorded a show" if we recorded something from television.

You can film or record a video, but you can only record voice. Film requires images. So, yes, you can say that you film a film. It’s a little redundant, though. I might instead just say I film (with no direct object) or say that I record a film or make a film. Hope that makes sense. I know it’s all “grabar” I’m Spanish, so I see your confusion.