audio signal passing through my body
Very nice example of interference. The signal could pass though, especially to high impedance and sensitive microphone input. With your body you are adding series resistance (range of some tens of kohms), but also resistance to ground that attenuate the signal. (it is actually more complex, as the signal is AC and and body is not pure real resistance, but a combination of inductance and capacitance too resulting in compex impedance).

I imagine that RF signal from the transmitter couples to your body and then excite the mic input.

To your last question, yes, your body can conduct also from a low voltage source, but you hardly power something through your body because you add too much resistance.

Your body is actually generating a small electrical signal (couple mV) that you can pick up by ECG.