Prompted by a comment thread, I was curious if my understanding of the
semantic differences between

> [nominal phrase]？  
>  [nominal phrase]なの？  
>  [nominal phrase]ですか？  
>  [nominal phrase]なんですか？

is actually correct or just a delusion.

(か？ and のか？ further complicate things so I've left them out to keep everyone
sane.)

# Scenarios

I conjured up a bunch of example scenarios and have tried to categorize them
and how each different type of ending works.

### Confirmation

When you are asking for something to be confirmed because you didn't hear it
or it was surprising...

> 「彼は医者になった」  
>  医者［○？ ｘなの？ ○ですか？ ｘなんですか？］

なの？ and なんですか？ seem like they are asking a redundant question to me. I would
not be surprised if this was me making a mistake, though.

### Referring to immediate states of things

There's a certain class of 形容動詞 which seem to behave differently, for example:

> ダメ ［○？ ○なの？ ○ですか？ ○なんですか？］  
>  大丈夫［○？ ○なの？ ○ですか？ ○なんですか？］

These 形容動詞 seem to accept simply ？.

However, ones which don't refer to the immediate states of things don't accept
？ nearly as easily, e.g.:

> きれい［ｘ？ ○なの？ ○ですか？ ○なんですか？］  
>  上手 ［ｘ？ ○なの？ ○ですか？ ○なんですか？］

(I can't seem to think of any 名詞 which allow just ？ aside from in the
confirmation usage.)

### Inference

Sometimes, you follow a statement up with a question asking regarding some
inference you've made.

> 「彼氏は病院で働いてる」  
>  彼は医者［ｘ？ ○なの？ △ですか？ ○なんですか？］

I think the latter three all work, but なの？ and なんですか？ seem to "flow" a tiny
bit better to me than ですか？.

### Question words

> 誰［○？ ○なの？ ○ですか？ ○なんですか？］

### Normal questions

> 彼氏は医者［ｘ？ ○なの？ ○ですか？ ○なんですか？］

### Other things

There are other things like rhetorical questions which use none of these
endings, so they are not included unless there ends up being a good reason.

# Comparing the endings

So, sometimes multiple things work equally well. Are there differences in
nuance?

  * There's the obvious difference in politeness between the non-です and です versions.
  * I really do not see a difference between ですか？ and なんですか？ in the cases I have them both marked as ○. This is unlike the non-question case: 「彼氏は医者です。」「彼氏は医者なんです。」, where the latter sounds more like you're making a stance on something or using the sentence as justification something.
  * When both ？ and なの？ are possible, なの？ seems more childish to me.

# The question

So, how much have I gotten wrong here? Are there other types of scenarios
worth considering? (Sorry for the long blogging question.)

I'm totally open to an answer which completely ignores my analysis and gives a
radically different one.
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nuances questions
The difference between [noun phrase]+[？・なの？・ですか？・なんですか？]
1. For a confoirmation to 彼は医者になった, both 医者？ or 医者なの？ work. But the formar is more associated with nuance of "Huh? Perdon me?" while the latter has more to do with surprise.
  2. きれい？ or 上手？ are fine.
  3. For a reply to「彼氏は病院で働いてる」, it's 彼は医者［○？ ○なの？] though the latter has more sense of inference.
  4. As a normal question (e.g."Excuse me, do you have a boyfriend who is a doctor?"), it's 彼氏は医者［○？ ×なの？］.

Polite versions are just parallel.
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I'd say that the ones you've picked are pretty regular semantically.

  1. ~？ and ですか？are simple yes/no questions used when you have no prior information one way or the other. You can also use them to confirm that you heard correctly. 
  2. なの？ and なんですか？ tie the question in with the discourse or prior assumptions. You've heard or gotten some hint that e.g. he's a doctor, and you want to confirm or express a nuance of surprise/disbelief/awe etc: "医者なの？""医者なんですか？". Likewise, if you'd heard that he was NOT a doctor, you'd use "医者じゃないの？""医者じゃないんですか？"
  3. I'd say that in each pair, ですか？ and なんですか？ are pretty much just polite versions of the others. 

All nouns and na-adjectives work fine before "？", by the way.

If you start looking at less commonly used patterns like か？, なんだ？ etc, it gets
a bit hairier.
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I agree with the comments from the other two answers. I am not sure how useful
this will be but as I looked into guidance on acceptable sentence endings a
little while ago (in particular when the zero copula, の and か can be used) you
might be interested to see what I found for “question statements”. As I
already had them I have kept のか？ and だ in but by all means disregard these
parts.

The most useful reference was “Da and the Zero Form as the Two Contracted
Forms of the Japanese Copula” by Mioko Miyama (which I got from Snail boat and
you can google). I have pasted the list I made using this paper of acceptable
endings for questions (excluding です) below.

**Acceptable stand alone questions formats per M Miyamoto’s paper** (Nb:
∅=zero copula)

Wh-questions:

誰が学生 な の？  
誰が学生 だ？  
誰が学生 ∅？  
か：  
誰が学生 であるのか？  
誰が学生 なのか？

Yes/No questions:

太郎が学生 なの？  
太郎が学生 ∅？  
か：  
誰が学生 であるのか？  
誰が学生 なのか？

The other points I think are relevant are:

_1. の-nominaliser／です_

As per the extract from Snailboat in Chat yesterday, there is some
“controversy”but の can be used (1) when the speaker wishes to include some
conjecture/attitude – touched upon by Dainichi - or (2)just as a plain
question marker (with no extra nunace).

With questions ending in ですか I think の is only used when including such
conjecture/attitude, because it is not acting as a question marker. So if, for
example, you are just seeking information (with no prior knowledge) then んですか
may sound out of place (I have an example and references).

I am not aware of any difference in politeness between questions and non-
questions using んです(か).

With なの I think the additional nunaces may be conveyed by intonation/emphasis.

_2. Nouns vs 形容動詞_

The paper I cited states that “although adjectives are not under consideration
here, da after nominal adjectival predicates behaves in the same way” . Based
on this statement and inquiries to native speakers, there is no difference in
the copular taken by nouns and that taken by 形容動詞.
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