This is has nothing to do with the noise removal process but with your encoding. In order to do any type of processing with an encoded audio file you need to
Decode the input file to PCM
Process PCM data
Encode the PCM into the desired output format
Please note that steps and 1 and 3 are completely independent. The decode is determined by the input file ...
I guess this probably just a mistake in your analysis code.
Quantization noise is white and for a noise signal it's uncorrelated to the original signal, so spectrum of the original noise doesn't matter.
I did repeat your steps and saw exactly what I expected: The quantization noise is white and the spectrum of the quantized signal follows the original signal ...
No such thing as a single frequency of the noise. That's exactly why it's called white; it has power in all frequency ranges, but not at a single frequency.
Finally, is there a frequency-domain representation of Gaussian white noise?
Yes, a constant power spectral density for all frequencies. That's like white light (which contains also a continuum of all ...
If your are using a linear time invariant lowpass filter (such as a Finite Impulse Response (FIR) or an Infinite Impulse Response (IIR) filter), and have negligible rounding errors in each operations then doing the lowpass filtering before or after the averaging will yield the same results.
Note that from an implementation perspective, doing the averaging ...
The output process is clearly zero-mean because the LTI system cannot add a mean to the zero-mean input process. The variance of the filtered process is given by
which results in $3A^2N_0/2$.