> My interpretation is that the energy of the universe exists in time and space, evolving across the dimension of time. But it has an edge called 'the beginning'.
Actually, Hawking's proposal was that there is no "edge". In his proposal, the 4-D spacetime of the universe has no boundary, just as the 2-D surface of the Earth has no boundary. What we call the "beginning" of the universe is more like the South Pole of the Earth: we pick it out of all the other points because of a particular property we're interested in, but it's not an "edge" any more than any other point is. (Note that this analogy, which Hawking used, is referred to in the article.)
Is the hypothesis still that the limit as time goes to zero still exists as a part of our universe? In your analogy, is the south pole still a point contained on earth or is it just a point you can get arbitrarily close to?
There is no "time" at the "South Pole" point of the universe, or sufficiently close to it. The spacetime geometry in Hawking's model is purely spacelike in that region, not split up into "space" and "time" parts the way it is now. (As I understand the model, the boundary of the "spacelike" region" is at the beginning of inflation.)
> is the south pole still a point contained on earth or is it just a point you can get arbitrarily close to?
> Is the hypothesis still that the limit as time goes to zero still exists
Note that in other models of the universe, the ones that have an "initial singularity" which can be thought of as "the limit as time goes to zero", the initial singularity itself is not part of the universe; it can be approached as a limit but never reached. (The reason is that spacetime curvature increases without bound as the singularity is approached, and the equations of GR break down at the singularity.)
One of the nice things about Hawking's model is that it totally avoids this problem; spacetime curvature is finite everywhere and there are no singularities and no points where the equations break down.
Actually, Hawking's proposal was that there is no "edge". In his proposal, the 4-D spacetime of the universe has no boundary, just as the 2-D surface of the Earth has no boundary. What we call the "beginning" of the universe is more like the South Pole of the Earth: we pick it out of all the other points because of a particular property we're interested in, but it's not an "edge" any more than any other point is. (Note that this analogy, which Hawking used, is referred to in the article.)