While that would fulfull all the requirements for a wormhole, it only goes one way. The classical picture of a wormhole allows for similar movement both ways. But to answer the second part of your post, nobody's sure, thus this forum. It is impossible to tell what happens at a black hole's singularity with current physics, even as advanced as they are. But if it is a wormhole, then this problem might be circumvented completely. At the center of a white hole you speculated that there may be a singularity. What you were thinking was probably correct, but a singularity, by definition, is a region of space where matter is infinitely dense. I would believe that at the center of a white hole there would be something exactly opposite this, an "anti-singularity" that emits matter in exactly an opposite fashion.

: Let's just say that the speculation concerning a : sort of transportation from a black hole to a : white hole is true, isn't that the same thing as : a wormhole? Does the fact that black holes have : a singularity in their middle make travel through : impossible (I'm assuming white holes have them, : too)?