Question: Are the foreign movies dubbed or subbed?
Question: This applies to the TV series as well as the Movie. How are the "watching the movie" segments filmed? Are they literally sitting in front of a large screen? In some of the TV episodes, Joel/Mike is seen pointing to something on the screen. And do they film each segment as one, or is it cut into different takes?
Chosen answer: They sit in front of a big screen -- or rather Joel or Mike sat. The puppeteers crouch down below the row of seats and hold up special black puppets to project the silhouettes. They did do takes for segments of the movies. I imagine it would be painful for the puppeteers to crouch for 90 minutes!
The robot puppeteers laid down on the floor and the human host deeply reclined in front of a piece of plywood cut in the shape of the seatbacks. There were TV monitors playing the raw cut of the film in front of them with their lines on a teleprompter. The theater screen itself was simply a giant green screen which had the movie video added to it in post production. Search for "Last Dance RAW" for a few behind-the-scenes and some in-theater excerpts from the last TV broadcast episode.
Chosen answer: Dubbed.
There might have been a technical reason they did not use subtitled movies, because the superimposed row of chairs and actors at the bottom of the frame would have covered up the subtitles.