there is a include folder in the where cygwin installed. when you
search include files they should search on these files. So set up
the include search path to that include directory.
I honestly don't know how much GUI support as a font end from the
cygwin. and you can't use the GTK like things , try to strict to the
xlib , it is supported by cygwin. for other GUI frameworks you need
to download the libraries separately.