|MadSci Network: Astronomy|
Good questions! There is significant evidence from supernovae and the cosmic microwave background that the energy of the universe is dominated by a vacuum energy or cosmological constant.
Under the simplest models for vacuum energy, the universe will eventually re-enter a phase of exponential expansion similar to the proposed "inflationary" period immediately following the Big Bang.
As for our bodies being torn apart by the expansion of the universe, check out this link.
By the "observable universe", astronomers simply mean anything that can be observed by us. Because light has a finite speed this means that we can't see anything further away than the speed of light times the age of the universe (roughly 10-15 billion years). If the universe is infinite (as suggested by current observations), then there's more to the universe beyond this limit, but it's too far away for us to have seen anything yet. Patience can solve this: wait another 10 billion years and you can see objects 10 billion light years further away than you can now. This is different from dark matter, which is matter within the observable universe which doesn't emit light but shows itself through gravity.
Try the links in the MadSci Library for more information on Astronomy.