Referencing other books in non-fiction, permissions etc

At the moment I'm doing a lot of reading for research for my non-fiction book. Now and then, in an article that says similar things to what my book says, I'll find a book referenced and a quote from that book or an argument that I'd like to use. Do I have to reference the author of the article as well as the book?
Do I have to say, for instance, "Jane Ding argues that white asparagus is much tastier than green and contains far more nutrients, and helps protect against memory loss. She quotes the extensive studies of Professor G. Prank, who has shown in laboratory studies that white asparagus significantly delays early onset Alzheimers by five years."
I want to quote Professor Prank; do I have to quote Jane Ding as well? Do I have to read Dr Prank's book in order to quote him?
There are many such instances where I find the book quoted more useful than the article itself.
If I do quote the article and/or book, do I have to write the author/publisher for permission, even if the quote is under the "fair use" mark?

What about quoting from a new edition of a book that is in the public domain?

Strangely, I had completely forgotten about this thread, on a similar subject, which I had read before and even posted on... the issue has arisen again, with a slight difference. I guess there's a lot to say (and ask) on the subject of quoting others (always with credit of course!).