It uses regen braking and coasting recharges the battery. Battery is almost always at 100% the way i'm driving. It will show you.
I presume if one did run it low, gas motor would fire up to recharge. yes.
Realistically you cannot drive it on total electric for very long around here. First good hill that you hit the gas motor fires up. I've tried. anytime you give more than a little throttle gas motor fires up.
I might have misunderstood your previous post about hypermiling. It sounded like you could keep going on the electric only with a very light touch on the throttle.