How to measure the voltage over a transducer? aka how to measure ultrasound
Am I using this instrumentation amplifier in a wrong way ?

Quite possibly (from your schematic).
As with any (maybe most) Instrumentation Amplifiers you need some DC bleed resistors down to 0 volts (mid rail) to remove bias currents because the inputs don't like to float: -

Bottom right is the picture I would reference in your particular case. Try 1 Mohm resistors.

What is a normal value for Rg ?


I wouldn't be all that keen on using a potentiometer.

Should I use a specific Shunt ? at the moment its just a 100Ohm
resistor

100 ohm sounds low for a piezo based transducer - something like 100 kohm upwards might be a lot better but, to protect your inputs from possible over-voltage, have 10 kohm resistors in series with the inputs to limit over-current into the InAmp.