Can humanity travel faster than the speed of light?
As far as we currently know, it is impossible for anything with mass and starting with a speed slower than that of light, to accelerate to a speed faster than that of light.
Humans have mass, and are currently traveling slower than the speed of light, so they would fit into this prohibition.
If it were one day discovered to be possible to travel faster than the speed of light, this would entail an overturning of our current understanding of physics, and its replacement with some newer, better understanding of physics. Whether humans would or would not be able to survive in any faster-than-light environment allowed by these new laws of physics would depend on what these new laws of physics turn out to be, if they even exist.
So the question at this point is unanswerable.