Translation:There is news again about journalists getting arrested in Turkey.
I don't think you do: unless I'm missing something, it could also be "there is news again about a journalist getting arrested in Turkey." (It's one of those situations where the speaker would have to clarify further, if the number of journalists were important: "bir gazeteci" or "birkaç gazeteci" or "birçok gazeteci" or whatever...)
How does this sentence parse?
I got as far as "Türkiye'de yine gazeteci tutuklandı", with the conjugated verb, but don't see how the "haberleri var" can connect to the above.
Shouldn't the first statement end in some kind of participle, e.g. tutuklandığı hakkında or tutuklanması için or something? Or at least diye somewhere?
How can "tutuklandı" modify "haberleri"?
you are actually right, I am not sure if the sentence we provided is grammatically very correct (although it might be used sometimes in daily speech). The best would be ""Türkiye'de yine gazeteci tutuklandı diye haberler var." It is probably best to get rid of it in order not to confuse learners.