1. Shall we have some pizza at the pizza house?

2. Shall we have some pizza at the McDonald's?

(Are both OK?)

3. Shall we see a movie at the movie theater?

3-1. Shall we go to see a movie at the movie theater?

3-2. Shall we go to a movie at the movie theater?

3-3. Shall we watch a movie at the movie theater?

3-4. Shall we watch the movie at the movie theater?

3-5. Shall we go to the movie at the movie theater?

(Are all expressions grammatical? Can we use both 'see' and 'watch'? Can we use the singular form as in ' go to the movie'?)

1 is fine.

2 is OK, but I'd delete "the" in front of "McDonald's"!!

3 through 3-5 are fine. They all mean somewhat the same thing. If "movie" is preceded by "a" you imply that there are several movies and you'll pick one later. If "movie" is preceded by "the" you imply that you've already chosen which one you want to see.

1. Both options are grammatically correct, but the more common and expected phrase would be "Shall we have some pizza at the pizza house?" This suggests going to a dedicated pizza restaurant or pizzeria.

2. While it is technically grammatically correct, it is less common and less expected to say "Shall we have some pizza at McDonald's?" McDonald's is generally known as a fast-food restaurant that serves a variety of items, including pizza in some locations. It would be more accurate to say "Shall we have some fast food at McDonald's?" to encompass the wider menu options available.

3. All of the expressions you provided are grammatically correct, but they have slightly different nuances and connotations:

3-1. "Shall we go to see a movie at the movie theater?" This suggests the intention of going to the movie theater specifically to watch a movie. It emphasizes the act of physically going there with the purpose of seeing a film.

3-2. "Shall we go to a movie at the movie theater?" This is also grammatically correct, but it sounds less natural to native speakers. It implies going to a specific location or theater that is showing a movie, but it may not convey the same sense of intentionality as the previous expression. It feels slightly more vague or less deliberate.

3-3. "Shall we watch a movie at the movie theater?" This expression is also grammatically correct. Instead of emphasizing the act of physically going to the movie theater, it highlights the activity of watching a movie within that setting. It doesn't necessarily imply the act of going to the theater as strongly as the previous expressions, but rather focuses on the movie-watching aspect.

3-4. "Shall we watch the movie at the movie theater?" This expression implies a specific movie that is currently being shown at the movie theater, rather than any movie in general. It suggests a specific plan to see a particular film.

3-5. "Shall we go to the movie at the movie theater?" While grammatically correct, this expression is less common and not as idiomatic. It implies going to a specific movie screening or a specific showtime at the movie theater.

Overall, you can use either "see" or "watch" to talk about watching a movie at the theater, and you can use the singular form for expressions like "go to the movie" or "watch the movie" when referring to a specific film currently playing at the movie theater.