Can a GFCI outlet be bad? If so, will it take everything on the circuit?
Yes, GFCIs can go bad over time.

And yes, they can block power to the entire downstream circuit. In fact, it's better that they do that than the other way around. You don't want a faulty GFCI providing power to a circuit that they're unable to protect. However, they're not guaranteed to do that, which is why you should test them regularly.