Hi Wolram,
These are very broad questions. I am not aware of even an ATTEMPT to explain why expansion continues. As you know, the favored view at the moment is that inflation was the original motivation for expansion. Subsequently, some unexplained form of momentum is supposed to keep expansion going. But it is a strange form of momentum, because nothing actually "moves".
Objects continue to become further apart because they were already becoming further apart. They were already becoming further apart because of inflation. And inflation apparently caused objects to become further apart from each other at almost exactly the Newtonian escape velocity.
In the absence of Dark Energy or other cosmological constant, a flat universe (which ours approximates) will expand more and more slowly, but never at a zero expansion rate. In other words, the expansion will asymptotically approach zero.
If the universe is even slightly above critical density (say, by a total of 1 photon), then it will stop expanding at a certain point in time and begin contracting. There won't be a "pause" per se between expansion and contraction, it will be instantaneous. However, the expansion will be extreeeemely slow for a long time before it reaches zero and then begins contacting at an extreeeemely slow rate, which will accelerate over time.
If Lambda (Dark energy or cosmological constant) is sufficient to overcome the total force of gravity, then expansion will continue to accelerate at a geometrical rate. That is the current mainstream projection regarding Dark Energy. Such a universe will never contract.
Jon