Not an electrician, so someone else may have better info.
Grounding provides an alternate path for the flow of electricity, so if a wire comes loose and ends up touching a copper pipe or something the current gets routed into the ground rather than into pipes or flammable wood or something.
Dispersal over an area isn't directly the goal, but it helps. By dispersing the current into an extremely large object, you don't really have to worry about the object building up a charge to the point where you can't flow current into it anymore.
Yes, you can dangerously energize the ground. You can dangerously energize almost anything with enough voltage. E.g. a Tesla coil has enough voltage to conduct through air. Don't try to test it (obviously), but I don't think a standard 110V house grounding has enough voltage to dangerously energize ground over any significant distance.