In the installation instruction is under 2.2.2.1 paragraph "Here's how to install Cygwin" written: After installation, start up a Cygwin shell and issue the following command: mount -f c: / assuming you installed Cygwin at C:\cygwin; otherwise change the drive and directory as appropriate. (So it definitely says / is at c: not at c:\cygwin. But later, when setting the environment variables it seems like it is assumed that / is at c:\cygwin.)

There are two things going on here: 1. You're mounting C: at / so you can refer to the whole drive with UNIX-style paths. 2. Cygwin automatically mounts parts of its directory tree under /usr.

In "2.2.2.2 Environment variables" is a table that says I should add C:\usr\bin to PATH. That directory does not exist. the directory C:\cygwin\usr\bin exists (assuming you installed Cygwin at C:\cygwin) but is empty. The C:\cygwin\bin directory seems to be the one meant. Should I add C:\cygwin\bin to PATH?

No. Add /usr/bin. Cygwin mounts \cygwin\usr\bin at /usr/bin.

The same table says that SHELL should be C:/usr/bin/bash. (Observe the '/' signs instead of '\'.) But bash is in C:\cygwin\bin (assuming you installed Cygwin at C:\cygwin). Should I set SHELL to C:\cygwin\bin\bash (does it matter if I write C:\cygwin\bin\bash or C:/cygwin/bin/bash?)?

As above. I think these instructions have worked for other people; my own system is in a slightly different configuration (which for various reasons we used to recommend). -- http://sc3d.org/rrt/ | humour, n. unexpected recognition