Yes, modulating the resonant frequency of that particular piezoelectric crystal is necessary.
A piezoelectric crystal has a very narrow range uncapable of emitting or receiving intelligible audio.
One of the ´You need...´ is a pool for testing, not a room.
Go head, keep building your receiver...
For unidirectional communicator, coarse transmitter 'block' diagram:
Voice mic--->preamp--->filtering--->modulator
Throat mic--->preamp--->vox--->oscillator--->power amp--->piezo element
Coarse receiver block diagram:
Piezo--->preamplifier--->filtering--->demodulator--->audio amp--->earphone*
*Forgot that one on the 'You need' list, also waterproof-depthproof.