|MadSci Network: Astronomy|
The edge of the universe could be defined as the distance that light has travelled since the universe got started. This is not a real, physical edge, but is simply the limit to the universe that we can observe. The age of the universe is thought to be between 10 and 20 billion years - so the edge of the universe is 10 to 20 billion light years way. As yet, no galaxies have been observed "at the edge of the universe", although they have been observed several billion light years away.
These observations can be thought of as looking back in time. The galaxies that are observed are younger than our own. This is one way that astronomers attempt to study how galaxies evolve in time. If one were to look to very great distances, one might hope to see galaxies forming, and going even further back, one can see the remnant of the big bang fireball, from which the whole universe emerged.
The effect you talk about, whereby more distant galaxies were receding more quickly in the past is certainly probable. Astronomers try and measure this effect to work out whether the expansion of the universe is slowing down enough (due to gravity) to cause everything to come back together in a big crunch. As yet, no conclusive measurements have been made. Where is the galaxy today? Well, yes - roughly twice as far away if the universe were not slowing down, and as old as our own galaxy is!
Try the links in the MadSci Library for more information on Astronomy.