The URL for Google call/voice

When are you consuming the minutes? In US (simplistically speaking), you pay when you are using your cell phone handset, both for incoming and outgoing calls.

If the call is not ringing your phone, but is using computer, I would say there would be no charge.

The backend architecture is the same. The Ggoogle Voice was an acquired company (Grand Central), which was slowly being integrated into Google architecture. Makes sense to not reinvent the wheel.

You don't have to use the cell phone either. Used to be you could route the call to Gizmo5 VOIP account and then connect directly to it over the internet. Now Google bought Gizmo5 as well (though my VOIP phone still works with it).

There is no way of switching phones for a call you initiate. Per this Google Voice Help article:

Keep in mind that it's not possible to switch phones during calls you make through your Google number

You can switch phones for a call your receive though

To switch phones in the middle of an incoming call, just press * while you're talking, and your other phones will ring