The derivation suffix in Türk|çe is makes an adverb out of a noun, doesn’t it? In the sentence

Türkçe mesaj yazıyorum.

I guess it is modifying the verb as an adverbial (but I’m not sure).

But that’s not all there is to it. Türkçe (with the adverb derivation included!) is also a noun and an adjective. As a noun it means about the same as Türk dili.

As a noun Türkçe derives regularly. But I can’t really understand its accusative use. I find examples of both:

Türkçe konuşalım!

 Türkçe´yi doğru konuşuyor muyuz?

How can one sometimes speak indefinite Turkish and sometimes definite Turkish? It doesn’t make sense to me. Is there a clue in the context which I can’t notice?

Can one say

?Türk dili(ni) konuşuyor

also?

This issue was probably in the first lesson of unit one but sorry it has slipped my attention.

Ah yes I have seen this too where there is the accusative case with Türkçe in some instances but not others. I wonder if it just depends on context. Or what came before the phrase. Like for specific Turkish. 

Bu Türkçeyi çok iyidir.

But if you´re only refering to the language generally maybe its just:

Türkçe konuştu

Just a guess from me Im sure it´ll be revealed soon though.