1. Ниоткуда не брала.

>> она ниоткуда не взяла эту цитату << stylistic better:: она ниоткуда не брала эту цитату (means it's her private creative, not another's people)

OLGA's version is a negation of my third: Она не "взяла эту цитату из ниоткуда"! (She did not "took it out of nowhere", there is a reference for it!).

Finally we can say: она взяла эту цитату из ниоткуда! из ниоткуда = "out of nowhere". As in: "Their team came out of nowhere and won the state championship." (from a dictionary). We say it as if "Nowhere" was an actual place, where she borrowed the quotation from. And we say so when she was NOT expected to find this quotation... ...or if we are unhappy with no source given for the quotation.

But you can say "ниоткуда не взяла" too! It sounds as a simple negation of previous statement (sort of: Она не "взяла" эту цитату, а.... - she did not "take" it, but instead....) As if you were "quoting" the original question, and then applying a negation to it as it is.