The GCW toolchain is exactly like a regular Linux toolchain, it just compiles MIPS binaries instead of x86/x64 ones.
In order to test the binary, you have to either copy it onto the real device, or, as Surkow previously mentioned, try it in a Qemu image we prepared (which still requires copying the binary onto the emulated filesystem). The GCW Zero OS (in both real hardware and Qemu) has always an FTP daemon running in the background, so all you need to do to copy the binary to the device is connect to it's IP address using your regular FTP client (ie. I use the FTP from Midnight Commander). You can do this over USB or Wi-Fi (I prefer the latter for no cable juggling involved). If for some reason you can't or don't want to use FTP, you can always just copy the binary onto a microSD card and then plug the card into the GCW's external microSD slot.
There are two ways to test the binaries. One is to prepare the final package (.opk), which will be automatically detected and appear in the GCW's menu system. The second (more preferable) way is to copy a raw binary to the GCW and then telnet inside the system (again, either via USB or Wi-Fi) and execute the binary from the shell. The system comes with tools like gdb and strace, so if you left the debugging symbols on, you can perform all the debugging on the running system.
As for your question about Windows - the toolchain itself requires a Linux x86 machine, however given you already have a compiled binary, you can FTP and telnet to the GCW from any operating system or device ever made that supports these protocols.
You are welcome to join our IRC channel
if you need further help/instructions.