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Yes, the US has redundancies in place to ensure continuity of operations (Called COOP) and to let potential enemies know that if they do attack we'll have the command structure left to completely annihilate them. This assured destruction is supposedly what is keeping anyone from launching a nuclear attack.
Yes this is one of the main reasons we are so dangerous. We have more than one way of defeating our enemies or making them suffer as much or more than we are. Just because you give a beating does not mean you will not be feeling it too.
Yes, exactly KN. That is why our nuclear deterrent is a triad. They figured when the developed it that a potential enemy, the USSR at the time, could definitely destroy one leg, possibly two legs, but never all three. So we have land based ICBMs, submarine based SLBMs, and bombers with both free fall and stand off nuclear capacity.