Southpa, quite a bit of what you have posted is correct, however, I must respectfully correct some of your information.
Actually, if the humming stops when you touch the strings, it is a almost a sure sign that the bridge IS grounded. Your body is adding additional grounded shielding to the circuit when you touch the grounded strings. Your body would not be providing the path to ground unless you were also touching something that was grounded to the circuit when you touched the strings. If the humming does not change, or gets worse when you touch the strings, that is sign that there is a grounding issue with the bridge.
Humming when you are not touching the strings, may or may not be the sign of a problem. Many guitar/pickup/amp/house wiring combinations hum more than others with the guitar turned up, and not touching the strings, when the shielding and wiring are just fine. Interestingly Fender Noiseless Strat pickups are very bad about this, even on a good day. But, as the majority of us tend to touch the strings when we are playing, this is really not an issue.
Actually it IS because the bridge is grounded (many other factors could apply as well) that you will get shocked if you touch something else that has a difference of potential to your guitar and amp's ground. If the polarity is incorrect between your amp and your PA system, this can cause you to get shocked when you touch something grounded on your guitar, and something metal like a microphone at the same time. Many of us know that wonderful feeling of being shocked on the lips while playing and going up to sing through an SM58, when this difference in ground exists between our amp and the PA.