That is called "hyperspace". Please note that that is a fantasy concept, used in several science fiction stories; there is no indication that such a thing actually exists in the real world.
I certainly HOPE so, but right now, it does not look likely. According to our understanding of physics and mathematics, it would be impossible for any object to travel AT the speed of light. Since...
Not as far as anyone knows. Ask again in 500 years.
This needs some clarification. If a person wishes to accelerate to the point where a friend back on earth would somehow be able to determine that...