If you lift the cover off your doorbell it may have a voltage rating on the terminals.
Most legacy doorbells have a 120v to 18-24vac transformer that’s often attached right on the circuit breaker panel or an oct box relatively close by.
And as previously suggested, if you had a voltmeter to read the open voltage at the doorbell button or the voltage at the doorbell when someone is pushing the button, that would be ideal.
Nope, no ground. The water provides a path to ground.
I used one in Belize. I never figured out what the siphon tube with mini shower head was for. The two wires just came through the wall and were wire nutted to the shower head wires. Pretty much like the picture I posted. It was an experience.