1)Control Panel -> Sound
2)Set playback device as your liking.
3)Set recording device to Stereo Mix only. ( Set as Default Device )
4)Enable your desired/operating microphone array at the same window segment also.
5)Go to Properties of that microphone , and find "Listen to Device" , check it.
6)If you check around more , sampling recording in same bit as your output , and 2 channels also may solve that microphone sound coming only from the left channel.
This is tested on this machine I'm typing. On Audacity or alike , just use the Stereo Mix. You can cover songs now , albeit it will be drunkish because you are also listening to your voice at the same time. I don't know though if Win 8 or your sound support
has "listening" property. Mine is Win 7 original and internet download , and my sound is IDT High Definition Audio CODEC ... and NVIDIA HD Audio as it writes in Device Manager , no else.