The home page for the Cygwin project is https://cygwin.com/.
There you should find everything you need for Cygwin, including links for download and setup, a current list of mirror sites, a User's Guide, an API Reference, mailing lists and archives. Parts are GNU software (gcc, gas, ld, etc...), parts are covered by the standard X11 license, some of it is public domain, some of it was written by Red Hat (or the former Cygnus Solutions) and placed under the GPL. You don't have to pay anyone to use it but you should be sure to read the copyright section of the FAQ for more information on how the GNU General Public License may affect your use of these tools.
State January 2016 this includes Windows Vista, Windows Server 2008 and all later versions of Windows up to Windows 10 and Windows Server 2016.
The 32 bit version of Cygwin also runs in the WOW64 32 bit environment on released 64 bit versions of Windows, the 64 bit version of course only on 64 bit Windows.
For a searchable list of packages that can be installed with Cygwin, see https://cygwin.com/packages/.
The Cygwin Setup program is designed to be interactive, but there are a few different ways to automate it.
If you are deploying to multiple systems, the best way is to run through a full installation once, saving the entire downloaded package tree.