Our teacher has given as an example question:

> なに いろ が すきですか？

But has told us that we cannot use the same construction for asking a question
about food, instead we have:

> 食べ物 は なに が すき ですか

What is going on here?

Elsewhere I've read things that suggest that 'naniiro' is a question word and
that 'nani' can combine with some words like that.

Is there a good linguistic explanation of what is going on?
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question
questions interrogatives
Combining なに　with a noun
I think maybe this doesn't have an answer yet because it's been answered in
the comments and also because your presumption is right: [何]{なに} can't
reliably be combined with just any noun, but it does so in certain compounds
such as [何]{なに}[色]{いろ} and those mentioned in the comments. In addition,
[何]{なに} combines with counters and temporal nouns to produce words like
[何]{なん}[台]{だい} and [何]{なん}[月]{がつ}. What you can't do is say, e.g.:

> 何[食]{た}べ[物]{もの}が[好]{す}きですか。X

This, however, is okay:

> [何]{なん} **の** [食]{た}べ[物]{もの}が[好]{す}きですか。
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answer
It's worth separating the two examples as examples of different constructions
to ask the same type of question. It will make more sense if you comprehend
the following:

> **X が (adjective/verb) か。**  
>  (X as subject「が」) (adjective/verb question「か」)
>
> なにいろが すきですか。  
>  ( _what color_ is the subject) ( _do you like_ is the question)  
>  What color do you like?

As you mentioned before, なにいろ is a sort of question expression asking _which
color_ or _what color_ or something to that effect.

This is related to, but not exactly the same as:

> **X は Y が (adjective/verb) か。**  
>  (X as topic「は」) (Y as subject「が」) (adjective/verb question「か」)
>
> 食べ物は なにが すきですか。  
>  ( _food_ is the topic) ( _what_ is the subject) ( _do you like_ is the
> question)  
>  As for food, what do you like?

That being said, it is possible to rewrite なにいろがすきですか as いろはなにがすきですか but it
sounds more natural in the first form whenever it is available depending on
the question. Likewise, it is possible to rewrite たべものはなにがすきですか to
なんのたべものがすきですか。
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answer