It is correct, but if i had to translate it back to German there seems to be more emphasis on "still not" and i would add "immer" to show that.
Ich habe die Zeitung immer noch nicht gelesen.
noch is one of the small words that can mean lots of things in different combinations.
Putting the object "die Zeitung" in first position is not the standard word order, either. That would need some justification in context, where "die Zeitung" is established information and connects to something said before. For example the answer to a question.
Kann ich die Zeitung und das Buch wegräumen? Die Zeitung habe ich nocht nicht gelesen.
Can I put away the newspaper and the book? The newspaper? I haven't read that yet.
Generally, the more important and new information comes at the end. This is usually close to part of the verb, because although the standard position for the finite verb in a main sentence is the second position, there are lots of ways to put a meaningful part at the end: the infinitive, participle, separable prefixes or the finite part of the verb in a side sentence. Less important things like pronouns are usually more towards the beginning.
In English the more important things are close to the verb, too, but that is usually soon after the beginning of the sentence. So word order tends to be reversed between German and English translations.
Du hast ihn mir gestern noch nicht vorgestellt, weil wir uns da noch nicht getroffen hatten.
You did not introduce him already to me yesterday, because we had not met yet then.
When I first read your reply, I thought, alright, I suppose "I haven't read it yet" sounds a bit more natural than "I didn't read it yet", so maybe "did not [verb] yet" is simply not a proper grammatical structure. However, going by a native English speaker's intuition, "I didn't know about it yet" sounds a lot better than "I haven't known about it yet" (this just sounds completely wrong). Anyways, if the English grammar here is so subtle, maybe it shouldn't be the difference between right and wrong since we're learning basic German, not advanced English.
I'm not a native speaker, but I guess "I haven't known it yet." is simply illogical, because you still wouldn't know, what you're talking about. If you do know now, then you can say that at a certain time "I didn't know it yet - at that time, but now I do."
This is what German school kids have to face in English class.
I think the difference is one of time. "I didn't know about it yet"/"I had not known about it yet" means that back then I still did not know it, but I do now. "I haven't known it yet" would mean that at the present time I still do not know it.
For whatever reason, though, "I didn't read the newspaper yet" sounds wrong. To express the corresponding situations of time, I would say "I had not read the newspaper yet." and "I have not read the newspaper yet."
The past participle, the ge- form, is the unchanged "infinite" part of the verb, as opposed to the "finite" or conjugated part.
Verbs with separable prefixes (like aus-) take the ge- in between ausgesehen (looked like).
Verbs with nonseparable prefixes (like ver-) take no ge- at all. verloren (lost)
Some prefixes can be both (like um-) with different meanings. umgefahren (run over) umfahren (driven around)
Participles can be turned into adjectives and nouns. They are then inflected according to case number and gender and article like adjectives (declension of adjectives).
Das gelesene Buch - the read book
Ein Ausgestoßener. Der Ausgestoßene - an outcast. the outcast (the one who has been cast out)