No, paraboloid also has positive curvature. Sign of curvature refers to whether all curves at a point are in the same half-space (saddles have negative curvature).
Why it should be 2D? Three-dimensional hologram would totally works for us. Something like The Matrix and 13th Floor combined... You have everything in 3D around you and just a tiny part of the Universe (where you are currently looking at), because it is not possible to simulate the full Universe (the energy since the Big Bang till now won't be enough).
All holograms only have 2 dimensions. They "trick" us into thinking the image you are seeing in the hologram has 3 dimensions. The idea behind the Universe being a hologram is that everything exists in flat space; however, it appears to us as being in 3 dimensions. Think of a video game, where you are moving around in a 3d world, but it's not really 3d, it just "feels" like it is.
Anyone interested in this can find an excellent lecture here http://m.youtube.com/watch?v=dEaecUuEqfc and of course by looking up leonard susskind's stuff on the black hole wars and universe as a hologram
What will happen when photons reach the outer boundary of the universe? Where time and space starts to slow down ... Will the photon also slow down, and then take an elliptic path? Might explain why the universe seem to expand in all directions.
I don't think it really applies in this case? It's pointing out a new scientific theory that raises a question. The author isn't poising a question him/herself
The universe is a strange place indeed.