First, there's a little misunderstading, I think
How does C++, which previously had no syntax capable of asking the OS for a window or a way to communicate through networks
There is no syntax for doing OS operations. It's the question of semantics.
suddenly get such capabilities through libraries written in C++ themselves
Well, the operating system is writen mostly in C. You can use shared libraries (so, dll) to call the external code. Additionally, the operating system code can register system routines on syscalls* or interrupts which you can call using assembly. That shared libraries often just make that system calls for you, so you are spared using inline assembly.
Here's the nice tutorial on that: http://www.win.tue.nl/~aeb/linux/lk/lk-4.html
It's for Linux, but the principles are the same.
How the operating system is doing operations on graphic cards, network cards etc? It's a very broad thema, but mostly you need to access interrupts, ports or write some data to special memory region. Since that operations are protected, you need to call them through the operating system anyway.
