Re opening quotes -- I think its OK to drop the specific citation link. No specific reason for this instance other than poor consistency on the part of the author ;-).
Agreed on consistency with citations.
Yes -- use of the "Notes" subheading is better than references -- as you say, it could then include something other than citations.
I'll delete the quote citations as I go.
I do think it's important to cite a not-so-famous quote in the text body which is from a specific source (e.g., NYT). I'll check for these.
As I said previous, I've found that consistent citations for internet based references is MUCH easier said than done. It seems more important to include all of the relevant information, than follow a strict format. Being that the section is labeled "Notes" we have more leeway.