I've always been stumped with the question of what lies beyond the universe, and I've come to the firm conclusion - void (i.e. completely empty). Does it make sense then to think of the universe as a finite 'blob' of atoms (the completely full) flying around each other in nothing? Furthermore, and more importantly, does it have a shape like a sphere?
It is not known. The universe has a finite age so we cannot see beyond the speed of light times that age (and taking the Hubble expansion into account as well). This means there is a 'visible universe' which defines a boundary of what we can observe. Information does not travel faster than light.
The whole universe is bigger than the visible universe, but we don't know how much bigger (it could even be infinite). However, as the universe contains all space ánd time, the stuff outside the universe does not contain both (try to wrap your head around that!)
As I mentioned it could be infinite, we could live on the three dimensional surface of a four dimensional ball (like an ant on a balloon) or our universe could be embedded in a higher dimensional multiverse (like string theory tells us).
We probably will never know because we cannot see past the visible universe.
No, beyond the universe does not lie anything. Not even space itself. You cannot be outside the universe because there is nothing to be in. The three (or four) dimensions you think of as space, do not exist outside of the Universe. According to the Big Bang theory not only matter was created during the big bang but most importantly space was created during the Big Bang.
There's another important quality of the Big Bang that makes it unique. While an explosion of a man-made bomb expands through air, the Big Bang did not expand through anything. That's because there was no space to expand through at the beginning of time. Rather, physicists believe the Big Bang created and stretched space itself, expanding the universe.
That is also why an inflationary phase where space expanded faster than the speed of light was possible. Matter cannot travel faster than the speed of light, but space can expand faster than the speed of light. So it is possible for two galaxies to 'appear' to have a relative velocity larger than the speed of light because in actual fact the space between those galaxies is expanding.
As to the shape of the Universe: You can only assign a shape to something relative to the space it is in. As there is no space outside the Universe, the answer to your question would be that the Universe has no shape.