I need to get similar information on the current windows and virtual desktops as that provided by the command-line app wmctrl. I s there some (C/C++) API header & lib-files that I can use?
Download the source code of wmctrl and study it. If you are making some free software with the same or compatible GPLv2 license you could take some code from it.
There is only one source file main.c and it seems to do ordinary Xlib calls, notably XGetWindowProperty calls wrapped in get_property
I'm very surprised you asked the question here. With free software, it is so much simpler and quicker to download the source code and study it.