I can record sound coming from my computer e.g. YouTube. However, the recording also picks up hazy, grey, room ambience noise. So, what I would like to know: is there any way to make Audacity do the re cording internally (connect directly to computer) so that it does no pick up the room noise?
Yes. Instead of choosing your computer’s microphone as your recording device, choose “WASAPI loopback” or “Stereo Mix”. See [u]this page[/u].
Depending on your operating system and drivers, your computer may not support WASAPI or Stereo Mix. The above page also lists several other solutions.