Help me solve this problem

Do you mean the adjective homogenous? It is correct in this position, in the same way that you could say, How sober are you? Sober enough to drive? The speaker is asking the degree to which a certain thing fits the description of the adjective. In your sentence, the speaker is asking to which degree the cuisine is homogenous.

"homogenous" in the sense you are using it was traditionally an error for "homogeneous". I still have misgivings about using it in this way, but Oxford Dictionaries reassures that it "can now be regarded as an established variant".

http://oxforddictionaries.com/definition/english/h

The Greek is ?µ??e???, so there's no extra vowel there, unless you count the accent for something.

This graph may be interesting:

http://books.google.com/ngrams/graph?content=homogenous%2C+homogeneous&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=

According to this, "homogeneous" is stil

Well, I think that case just be used in exclamation sentence, such as: '' How lovely you are!'' ?

Ti?u C?mWell, I think that case just be used in exclamation sentence, such as: '' How lovely you are!'' ?

That is an exclamation. How lovely are you? would be a question - admittedly a very unlikely one ever to to be asked.

Ti?u C?mIn the sentence ''How homogenous is national cuisine?'', there is something impossible. How can adj appears in that position? I think it must be a noun.

No, no, no! It's not a noun. "homogenous" is an adjective. "How" is an adverb that asks "to what degree".

How pretty is that picture? ~ To what degree is that picture pretty? (Very