Georgina,
You ask, "A question that comes to my mind is; Can the shape of the (medium of)space be changed faster than light can travel through it?"
What medium? Light propagates in a vacuum.
"If it can then there is the possibility that a phenomenon could be communicated faster than light speed."
That's how the worm creatures in Herbert's *Dune* series traveled faster than light -- they 'folded' space under the influence of some chemical. In the real world of relativity, however, space is not a physically real phenomenon independent of time; length contraction and time dilation guarantee that proper time seems to pass at the same rate for every observer everywhere in the universe, such that the laws of physics are uniform. One way to look at it, is that between photons at antipodal points of the universe, there is no duration.
Tom
