The only way this would happen would be if the internet would somehow be affecting the safety of the nation. If this began to happen, the final call on this issue would have to climb it's way up the chain of command, and since this is not really what the FBI is all about, the decision would end up with the Department of Homeland Security.
They can do whatever they want. The FBI will be shutting down the Internet for computers that has DNS problems and it sucks, because sometimes my computer has DNS problems. I don't know why. If the Internet was affected the safety of this nation, like Pieman117 said, then there is a chance that the Internet will be shut down.
Internet is a network of computers. They can't control servers and connections in other countries. eg: china, since china have their own cables and satellites. If they wanted to shut down others' too, they have to destroy all the satellites, but that would be stupid.
Yes. There was actually a proposal to give the president an "off switch" for the internet. This would be used to stop all incoming connections if there was a big enough threat. This was never put into use for several reasons: It would be very easy for hackers to exploit this. They would simply have to access the switch to turn off the internet. Or they could just set off a false alarm. After you turn it off, it would be very hard to start it up again.
I'm technologically behind due to laziness and rebellion, so I don't know the actual answer to this question. But I do wonder if "SOMEONE" does indeed have an off switch to this thing or an actual "plug" that could be "pulled". If such a thing were to happen immediately, I suppose we could survive. But I do wonder about what would happen when everyone and everything is eventually plugged completely into this "Matrix", and the switch gets turned off or the plug pulled. I suppose I shouldn't worry about it, because if it happens in my lifetime I'll probably be too old to care. Still, being addicted to drama or nightmare scenarios it is hard for me not to think about this.