Hello I know this might be more of a signal processing sort of question but I was just wondering if there was a way to use a Piezo sensor to record vibrations store the data and use some form of signal processing code to play back the vibrations picked up from the Piezo in its original analog form. Thanks for any input!
Piezo sensors tend to have quite non-linear response curves, so your "audio" will sound pretty odd although many of the old tape recorders etc. had a "crystal microphone" that didn't do too bad. It depends on what frequency range you want to record/look at. Remember you need to sample at better than twice the desired frequency to get a decent "recording" (see Nyquist rate).
You can certainly do that although as already mentioned it may not sound as good as when using a microphone. I did many years ago make an acoustic guitar amplifier using a piezo sounder and it worked ok. What you need to do is to use a charge amplifier on a body that can pickup sound waves i.e. a guitar or a tabletop or so. Just by itself I am not sure it will work but it may be worth a shot. here is a nice circuit showing a charge amplifier:
For the opamp you want to use one that has really (really) high input impedance and probably also a high gain bandwith. In this circuit a TL072 is used which is an excellent choice: cheap, high impedance und high gain bandwidth (i.e. it is fast!).
You should definitely give it a shot.
edit: you even are mentioning 'vibration'. If I remember correctly I did tape the piezo to a table top and was able to amplify the noise generated from a finger (not fingernail) lightly dragged across the table so it was quite sensitive.