OK, this post started out a lot longer, but I answered some of my own questions by scouring the conjugation tables at the back of this book. Otherwise, the explanations were non-existent in the text.
This one, though, I was not able to solve on my own:
რა გადის კინოში? დღეს ახალი კინო გამოვიდა
What does this even mean? It looks like it says "What is going out to the movie theater? Today a new movie theater came out." I don't understand either half of this. The initial question seems bizarre and the answer isn't much better. The only way I can think to have this make sense is if გადის means "to play" in the sense of a movie playing/running/appearing, and in the second part if კინო either refers to the movie itself and not the cinema or if გამოვიდა means "to open", which I doubt.