Re: Shall we see / watch a movie?
I'm not sure if I'm not reading Philo correctly (entirely possible) or if I simply completely disagree.
I'm in complete agreement with 5jj. I would never suggest we "watch" a movie if I'm asking my friend if we should spend our evening at the cinema.
A: What do you want to do tonight?
B: I don't know. Want to go see a movie? -- Clearly a trip the cinema.
B: I don't know. Want to go watch a movie? -- Not natural, unless you add something like "at my house, where I have a ton of movies on DVD."
B: I don't konw. Want to watch a movie? -- Implies you have movies at home to watch.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.