Noise overlapping speech

Hello there. Recently I’ve been trying to clean up audio recoding, but I’m having a hard time doing it due to some parts having noise overlap the speech.
There are 2 main sources of noise:

  1. PC fans (the sound of air moving)
  2. Lying nearby headphones, with a distorted sounds of music leaking out

For the first one I recorded sound of fans in a quiet room, then used it as a noise sample. For the second one, since I know what songs were playing, I just feeded the whole, good quality, song to the “get noise sample”, then applied noise reduction to the according part.

The results are okay, but far from good. Another problem I have is that while some settings seem to cut out noise decently, they also make loud speech sound like person is talking through a pipe.
Am I approaching it the wrong way? What steps can I take to improve my results? I’m new to audacity, so any advice would help.

You may be able to reduce the fan noise a bit with the Noise Reduction effect if (a) the fan noise is fairly constant (b) the fan noise is fairly quiet. Don’t expect miracles. Noise reduction is a balancing act between reducing the unwanted noise and not doing too much damage to the sound that you want to keep.

The music is probably best left alone because it will overlap the frequencies that you want to keep and it is constantly changing, so there’s no way to create a profile of the noise that can be distinguished from the profile of the sound that you want to keep.

There’s a very good reason why people record in quiet studios.

I was thinking that if I created a music track with the same level of distortion to create the same frequencies (it is possible in my case), and applied it precisely as a noise sample (meaning that the 1st second of my selected range has the same sounds as my distorted song sample + some speech, i.e. they are synced) it would be able to clean it up pretty good.

Is my assumption wrong? Would it at least help? If so, how much?

Basically, assuming there were two mics recording at the same time: my mic, and some magic mic that only picks up unwanted sounds, wouldn’t I be able to use magic recording to clean up the noisy one?

A noise-gate may be of use in squelching sound leaking out of headphones which is being picked up by the mic, but can only cut noise when the performer is not singing. You can get a free noise-gate plugin for Audacity here.