Erroneous results from ADC and piezo disk
Your battery does not share a common ground with the rest of your circuit. Its negative end is connected to the ADC's ground, but neither it nor the ADC ground are connected to the ground everything else references. Without a common ground reference, you're not going to get sensible results

If all you want is a stable voltage reference, you don't need to use a battery - you can use a high accuracy voltage regulator or precision voltage reference powered from the system's 5v supply. In either event, connect all grounds together.

You'll also want to bias your piezo element to half the reference voltage, with a resistor divider, so it has a resting point in the middle of your ADC's range.