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I don't really see any difference between false and NG.
For example:
Text: Album covers illustrate modern society.
Question: Record companies try to use album covers to illustrate modern society.

Because "record companies" is not given in the text, therefore, I don't know whether record companies use them to illustrate modern society or not, so it's not given.
But the answer is false, which I guess is because the text did mention modern society, and it was album covers that illustrate it, not record companies. So it's false.
I don't really think there's a huge difference between false and NG, they are kind of the same to me. Any advice on a deep understanding on this two options?

Another Example: The Question: I think the answer is False, because Michael is talking about himself, he doesn't say anything about other album pictures, "too many album pictures" is not what Michael means. it's a warped twisted way to distort what Michael says. I think it's false. But the answer is not given.

False = the opposite is stated
Not given = it doesn't say

Therefore - a very simplified example:
Text says "coal is black"
Questions:
Coal is blue - false
Coal is used to produce energy - not given

Your examples:
1 - record covers. I would say that it is not given. The text should be considered fact for the purpose of the questions. So album covers illustrate modern society - but there is no mention of whether this is intended by record companies or not. If the answer key is telling you this is false it is either a mistake or you have not isolated the complete part of the text which gives the answer.

2 - Michael. I think you have the right interpretation of the question, but the wrong interpretation of the terms false and not given. Michael is, as you say, talking about his own work of designing album covers - not album covers in general as the question is about. Therefore it is not given. It would be false only if he said "too many album pictures reflect the music and not the artists" - i.e. the opposite of the question.

I hope that helps - but if you are still unsure... perhaps you can upload the full passage and questions.