I think the 'problem' is that your questions assume that our current world-view is radically incomplete.
In answering the question 'does our universe move' you need a point of reference outside out universe. The way we see the universe now it is impossible to find a point of reference outside our universe, hence the question makes no sense given current scientific knowledge.
What would be needed is the discovery of something radically different, not outside our universe but merely far away from the galaxies and such. However, such an idea has no basis in the real world, and as such your questions and ideas sound like you are just coming up with stuff.
I guess you could answer the question with "All relevant point of reference gives a velocity of 0" which would be the same as saying that the singularity can't move.
This message has been edited by Melchior, 08-27-2004 09:58 AM