"Today I will present you the Turkish cuisine."
Translation:Bugün size Türk mutfağını sunacağım.
Is it "a double effect"? So first it is a compound noun (or whatever you call it) and for this reason we need an "i" at the end of the mutfak. and for the second we need an accusative because we mean a specific thing "THE Turkish cuisine". Do I see is correctly? Is that the reason for the double ending "in + i"?
The Turkish looks fine to me, but the "English" is not native-speaker English. It's the way a new Hungarian, say, immigrant to America would say it. To be literate, you have to say something like "Today I will present The Turkish cuisine to you" or "Today I will present you with Turkish cuisine." I realize this is not an English course, but if you want to be taken seriously by adult students, you have to get the English right.
Names of languages are always nouns but you can see them used like adjectives like in the case "Türkçe Kitap" which means "book in Turkish". This doesn't have the same meaning with "Türkçe Kitabı" which means a "book which teaches Turkish". In the former case you see a noun pretending as an adjective since "Kitap" doesn't have any suffix. But actually even in that case Turkish grammar doesn't take it as an adjective. This is another type of noun phrase which is called "takısız isim tamlaması".
In case of nationalities you need to use them as adjectives.
Example: İngiliz futbolcu
This exactly means the soccer player's nationality.
But check the example: İngiliz atı
Here we need the suffix "-ı" for "at" (horse) since it is not a nationality, it is an origin, a race.