Usage frequency between "at" and "in" with sample situations

As far as I know, "At" is commonly used when you are talking about a place as a venue or establishment where an activity, service, or facility is available or takes place, while "in" mainly indicates physical locations.

I don't think most of the following sampels are incorrect which one you use. At the same time, however, I don't think both of them are used with the same frequency either(it could be my bias though). Even if both are acceptable, you would hear one more ofen than the other or prefer one over the other when you say. So I just want to know your tendency in the examples below.

So if there are quizzes like the following, the answers would be:

1. The facilities at/in the American embassy are really nice. ->at
2. There's a new movie at/in the theater. ->at
3. There are beds at/in some theaters, so you can even sleep. ->both?
4. There's a huge screen at/in the theater. ->both?
5. Food is available at/in the theater. ->at
6. The cafe owner keeps a cat at/in the cafe ->in
7. There are so few tables at/in the cafe ->in

Which ones would you say in the situations?

at is for location, to be located at a place
in means inside of the place

Sometimes, you need to make the distinction.

Examples: Location: Food is available at the theatre.
Inside: The food is in the theatre not at the plaza outside.
Inside of: The cat lives in the cafe.
Location: The cat lives at the cafe, not at my house.
Location: There's a huge screen at the theatre.
Inside: There's a huge screen in the theatre.

And so forth.