If I have a piezoelectric crystal and apply pressure to it , it will be deformed and a voltage between its 2 ends will be generated.
Nope. When you apply pressure, which deforms and this causes the crystal to gain charge. So, basically, a piezo acts as a current source, and the current it generates is proportional to the rate of change of deformation. In fact, in actual circuits you have to use charge amplifier (or integrator) to measure the force/pressure/displacement.
Is the voltage generated due to its deformation or due to the
Suppose the piezo crystal has a surface area \$A\$. For the pressure you apply, there will be a force that will be acting on the crystal which will deform that in a particular direction and so it will generate current in that direction.
If I continue to apply the same pressure and it doesn't get anymore
deformed will there still be voltage?
No, because at some time the force that you applied will be balanced by the force which is generated by the stiffness of the crystal. So, your crystal will stop deforming and hence, there will be generation of current, so you cannot get any voltage.
If I stop applying pressure, it will return back to its initial position. Will voltage be generated?