> Q. How do we know that the universe expansion is really the explaination for the observed redshift of light from stars.

There is no other mechanism that can lead to the observed redshift/distance relation.

> As i understand it, space is a quantum soup of virtual particles.

It is not, this is just a myth in popular science descriptions.

> is it possible the magnetic and electric permeability of free space is changing over time?

If the chance has an effect on the universe then it also changes the ratio of wavelengths from different spectral lines, something we would observe.

> Q. If one has crossed the event horizon of a black hole, is one traveling faster than light and thus going backward in time wrt the outside universe on the other side of the event horizon?

How you describe the motion depends on your (largely arbitrary) choice of coordinates for the inside, but it's not time travel in any of them.