Re: post #1, and aggregate graduate rankings (per U.S. News), I have found this listing useful. It is certainly not perfect, nor is U.S. News. Note that the ranking (first link) is a few years old; below, I have posted this site’s new departmental listing, published with U.S. News 2015 data. The second link lacks the aggregate ranking – maybe they will reconfigure that table soon:
http://publicuniversityhonors.com/rankings-academic-departments-private-elites-vs-publics/
The 2015 selection (not comprehensive) of top departments; private institutions only mentioned in a tie: