Noise in Oscilloscope

Dear members,
I am using a TDS2024C scope and recently encountered the following two issues for which I do not have any satisfactory explanation.
1. I am trying to measure the output of a hydrophone (piezoelectric) using the scope. I connected a BNC to the scope from the output leads of the hydrophone (floating unit not grounded). When the hydrophone is not powered, just connecting the BNC to the scope displays a noisy signal with pk-pk to voltage of 10/20 mV. I understand that connecting the negative signal lead of the circuit to the BNC brings it to scope ground reference, so what is the reason for this noise even when the circuit is dead ?

2. While trying to figure out the above, I observed that if I just touch the center of any input terminal, with a wire while touching the other end of the wire by hand, it displays a periodic waveform in that channel. What is the reason for this?

Any help in this regard will be highly appreciated

I think the periodic waveform is mains hum, because the "hot" wire of the scope does not have continuous coverage by a grounded shield.