1. What are the differences in meaning between these three sentences? 

> えいがはなにを **みましょう** か。  
>  えいがはなにを **みます** か。  
>  えいがはなにを **みません** か。  
>

  2. Does the last sentence even make sense?
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usage questions
What is the difference between 「何を...ましょうか」, 「何を...ますか」 and 「何を...ませんか」?
I will answer first your 2nd question, and after that I will address your 1st
question.

* * *

## **2. Does the last sentence even make sense?**

No, the 3rd sentence does not make sense. Only the 1st and the 2nd sentences
make sense:

> えいがはなにをみますか。Regarding movies, what will [you/we] watch?
>
> えいがはなにをみましょうか。Regarding movies, shall we [you/we] watch?

Using ません or ましょうか turns the question more into a proposal:

> ラーメンを食【た】べ **ませんか** 。Won't [you/we] eat ramen?  
>  ラーメンを食【た】べ **ましょう** 。Let's eat ramen.  
>

It does not make sense:

> ~~えいがはなにをみ **ませんか** 。Regarding movies, what movie won't [you/we] watch?~~  
>

To propose the listener to watch a movie with ませんか or ましょうか, you can also use:

  1. なにか (it means "something"), and drop を: 

> えいがは **なにか** みませんか。Regarding movies, won't [you/we] watch some [movie]?  
>  えいがは **なにか** みましょうか。Regarding movies, Let's watch some [movie]?  
>

  2. The actual title of the movie: 

> えいがは **Star Wars** をみませんか。Regarding movies, won't [you/we] watch Star Wars?  
>  えいがは **Star Wars** をみましょうか。Regarding movies, Let's watch Star Wars?  
>

  3. Remove えいがは and use えいが as the object of 見【み】る directly: 

> えいがをみませんか。Won't [you/we] watch Star Wars?  
>  えいがをみましょうか。Let's watch Star Wars?  
>

* * *

## 1. What are the differences in meaning between these three sentences?

If you compare the three sentences used as a proposal (as explained in the
previous section), **they mean the same, but the difference is in the _level
of politeness_ of each proposal**. In the Japanese language, in general, the
_less_ direct you are the _more_ polite you sound. So, arranged from the
_more_ polite to the _less_ polite:

> 1) えいがは **なにか** みませんか。Regarding movies, won't [you/we] watch some [movie]?  
>  2) えいがは **なにか** みましょうか。Regarding movies, let's watch some [movie]?.  
>  3) えいがは **なにか** みますか。Regarding movies, will [you/we] watch some [movie]?.  
>

(1)(ませんか) is a _negative_ sentence and therefore it is the most _indirect_.
For this reason, it is the politest one.

(3)(ますか) is a _positive_ sentence and therefore it is the most _direct_. For
this reason, it is the less polite. To be honest, I don't think it is
frequently used to make a proposal because it sounds too direct. I guess it is
more used as a regular question.

(2)(ましょうか) is somewhat in the middle. ましょう is the standard grammar to make
proposals in Japanese. Worth noting that if you don't add the か to ましょう, it is
still valid as a proposal sentence, but ましょうか is politer than ましょう because,
again, turning it a question by adding か makes it more indirect and therefore,
politer. So, adding ましょう to the comparison, from the **more** polite to the
**less** polite:

> 1) えいがは **なにか** みませんか。Regarding movies, won't [you/we] watch some [movie]?  
>  2) えいがは **なにか** みましょうか。Regarding movies, let's watch some [movie]?.  
>  3) えいがは **なにか** みましょう。Regarding movies, let's watch some [movie].  
>  4) えいがは **なにか** みますか。Regarding movies, will [you/we] watch some [movie]?.  
>
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えいがはなにをみましょうか implies an invitation. しましょう(か) means "Let's". It means
(私達は)何の映画をみようか("What movie should we watch?" Or "Let's watch a movie. What is
a good movie to watch?"),

えいがはなにをみますか is a question. It is "What movies do you watch?"

えいがはなにをみませんか is also a question. You are asking someone what movies he doesn't
watch. However, it is rarely used and a bit unnatural. I say どんな映画は見ないのですか.
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