Hi msafrin -
these are indeed some of the most fundamental problems of cosmology. There are many theories as to what is "outside" the Universe. It all depends on how you see the Universe in itself. If the Universe originated from "something", then it might indeed be growing "inside" this something. But if our Universe is a closed entity which has no clear beginning and no end (which several scientists actually believe), it would be useless to try to define what is on the "outside".
As for the time reversal idea, there is something in our Universe called entropy. It is a feature (basically, the second law of thermodynamics), which states that any system will fall into gradual disorder as time passes. This is (to put it simply) because it takes energy to keep any organized structure intact, and this energy has to come from somewhere. So the entropy for the Universe as a whole is constantly increasing. Imagine a cup breaking into pieces: indeed, if you film it you can play the film backwards and see the cup become whole again. But there is no way the cup would accidentally put itself back into one piece, even if you somehow "reverse" time - because time is (most likely) not reversible in this way.
Now, the real issue with that is that while it is easy to see time as something flowing "forward", it is not so straightforward to reverse it and expect things to happen backwards. (Se our "
Arrow of Time Hypography" for more about this).
But I might be digressing here. You ask if the expansion as we see it originates from the center of the Universe, and that it could theoretically be found.
Well, yes - and no. Theorists do not agree on this issue. Even if the Universe once came from a "singularity", it is important to remember that this singularity <b>was the entire Universe</b> at the time of the Big Bang. What has expanded is the entire Universe. So the center of the Universe does not really exist (what I am trying to say is: the entire Universe does not have a center). For there to be a center, you would have to have a perfectly spherical Universe inside which everything moves away from an absolute center towards the edges. But it all depends on what kind of Universe we live in, really, and this is such a difficult question that I would be ignorant if I try to take this discussion further myself...perhaps other can help out.
Some very interesting books on the topic are:
John Barrow and Frank Tipler: The Anthropic Cosmological Principle
John Barrow: Impossibility (this one is really great)
Stephen Hawking: The Universe in a Nutshell
Martin Rees: Just Six Numbers (Our review:
Just Six Numbers)
...and I have just finished reading Martin Rees' latest, "Our Cosmic Habitat", in which he argues that our Universe may indeed just be one among a whole ensemble of Universes in a "Multiverse". But this is _very_ speculative. In essence, he argues that not only does our Universe not have a center - but it is not even a center in itself. It is part of something bigger. Which sort of would be related to both your questions...
Hope this made at least some sense!