Can I use a PC Microphone in a PIC with ADC?
The electret requires a biasing circuit, you cannot connect directly to the PIC. The signal would be very small so you'll need an instrumentation amplifier. The PIC ADC lacks the sensitivity for the raw signal (see #2 below).  You'll also run into trouble with aliasing so you'll need an analog low pass filter.  

Some other things to consider:


The best sampling rate you can probably get is 10-12 kHz, which means you can only get up to 5-6 kHz due to Nyquist, which is not nearly enough for music.  Most hearing aids do 16 kHz, and that is for old people who are missing most of their high frequency hearing already.
The best resolution you can probably get is 10-12 bits.  Which means you will have a high noise floor, so only really loud sounds will make it through.  Or if you amplify a lot, loud sounds will saturate the input.
FFT is a demanding calculation, you would have to use an 8-point or 16-point FFT which probably isn't the resolution you were hoping for. Maybe their dsPIC33s can handle more, but streaming FFT calculations is out of the question for most of their PICs.


You need more beef, consider doing it with a Rasberry Pi or something with Linux and an audio jack.  Doing that in real time will be quite challenging in itself, without having the hardware limitations of a PIC.  Don't get me wrong.  I love PICs, but they just aren't suited for audio, let alone music.