Where does the matter that gets sucked into a black hole go?
Black holes are fascinating things, but one of the frustrating things is how little we know about them. Your question about where mass goes when it falls down a black hole is one that, if you could answer it, you'd be guaranteed a Nobel Prize. We do know that as a black hole swallows more mass, its "event horizon" increases in diameter. As you may know, the event horizon is the real mouth of the black hole, the point at which spacetime becomes so warped that no light can escape. But as to whether the matter remains in the black hole in some kind of super-compressed state, or whether it travels somewhere else in a worm hole, we just don't know. Stephen Hawking as discovered a form of radiation that actually saps energy away from a black hole (called Hawking radiation), and this will gradually cause the black hole to evaporate, and eventually disappear altogether. Current experiments are trying to find out if this Hawking Radiation carries any information about the original matter that fell down the black hole. But for now, we can't say. As for white holes, they have fallen out of favor in the last few decades. We see no evidence of any white holes in our universe, and we've been able to see most of the way back in time and out into space at this point. It's possible that a white hole actually started the Big Bang billions of years ago, and in fact, black holes that form in our own universe may end up giving birth to parallel universes, starting off new Big Bangs. It's a great idea, but we've no way to prove it yet.Is it possible to go through a black hole?
I'm afraid that the idea of traveling through a black hole is still well in the realm of science fiction. It may be possible, but we have absolutely no idea how.Is stuff on the other side of "the edge" of the visible Universe not visible to us because it is expanding so fast that the light has not had time to travel to us since the big bang?
The short answer is "yes." Astronomers sometimes talk about the "visible Universe" or the "known Universe" to talk about the area of space that it's possible for us to observe. But it's a little more complicated that there just not having been enough time for light to travel to us. As you may know, the farther away something is, the longer light takes to travel to us, therefore the farther back in time we see it. The Andromeda Galaxy, for example, is 2 million light-years away, so we see it as it appeared 2 million years ago. Going farther out, we can see galaxies billions of light-years ago, from a time when the universe was young. If we look far enough away (which we can with our microwave satellites), we can see a time so far in the past that no stars had yet formed, and the entire universe was a big glob of hot fluid and very little structure at all. And here's the problem - before that, the universe was actually dense enough to be opaque to light, so no light can possibly get through. Astronomers call that the "curtain" - there's an impassible opaque wall surrounding us in all directions if you look far enough away (and far enough back in time).Is S2 or is Sgr A the black hole which is thought to lie at the center of our galaxy? How large is it?
So is it possible that there are galaxies (that exist today) that are farther away than that curtain? Sure. But we'll never have any direct way to observe them. Nor can they see us; to them, we're behind that curtain. Even if it weren't for the curtain, we still might not be able to observe the entire universe. Like your letter implied, the farther away objects are from us, the faster they seem to be expanding away from us. Astronomers really think about that as the Universe itself - space itself - expanding in between the galaxies. If a galaxy is far enough away that the space between us and it is expanding faster than the speed of light (and actually that doesn't violate Einsteins's laws), then we'll never be able to see it.
S2, a relatively faint source detected in the infrared, is not thought to be the black hole -- it is a star with a very large proper motion, meaning it is moving around the much more massive nearby black hole. However, it's not altogether clear what the "S" sources are that are seen in the inner arcsecond of the Galaxy--probably they are stars, but they may be exotic stars. Sgr A* is the name of a radio source which coincides spatially with the dynamical center of the Galaxy, and which also coincides (within the pointing errors) with a flaring X-ray source seen by the satellite Chandra. This is a very exciting result and significantly helps bolster the case that Sgr A* is a black hole.
Technically, the "size" of a black hole is infinitesimal (a point in space-time), but it does have a "width" associated with it known as the event horizon. Nothing inside the event horizon can escape the gravity of the black hole, not even light (that's why it's black).
The mass of the black hole at the Galactic Center is measured, by the motion of stars and gas around it, to be about 2.6 million times the mass of the Sun, or 5.2 x 10^39 grams. The event horizon, which depends only on the mass, extends to a radius of 7.7x 10^11 cm (= 7.7 million km = 4.6 million miles) from the center. That's a radius of about 20 times the distance from the Earth to the Moon!