What is the difference between "noch nie" and "noch nicht" and simply "nie"?
Is this related to whether I expect the negation to change in the future or not?
It's the difference between "I have never" and "I haven't yet".
If you have never, for instance, been to Brazil, you can say both:
"Ich war noch nicht in Brasilien."
"Ich war noch nie in Brasilien."
Both work fine. "Noch nie" places more emphasis on the fact that you've never been there.
If, however, you make a statement that is true only for a given scope of time, you can't use "noch nie":
"Ich habe (heute) noch nicht gefrühstückt."
"Ich war (dieses Jahr) noch nicht in Brasilien."