"These measurements, confirmed by the Cosmic Background Explorer satellite in 1989 and 1990, suggest that our galaxy and its neighbors, the so-called Local Group, are moving at 600 kilometers per second (1.34 million miles per hour) in the direction of the constellation Hydra."

Does this speed look about right for the Milky Ways movement?

Off the top of my head the 600 kms per second is the number for our motion relative to the cosmic background radiation. So yes that's about right. Motion must

*always* be given in relation to something.

Remember we are all laymen in this discussion. I had undergrad level courses on the physics and math of this but I only have a tenuous grasp of it. Note this well: you have little to no clue what you are talking about.

Space all around us is moving at the speed of light but we are not moving with that space how is that possible

This is incorrect. Spacetime is expanding. Space isn't moving the amount of space between objects is getting bigger. Percy gave you the numbers earlier. Since the amount of expansion depends on the size of the space expanding it doesn't show up unless you are talking about very large (intergalactic) distances.

To maybe help by making it simpler: if a distance enlarges by 1 % then if the distance is about a yard the expansion is somewhat less than half an inch but if the distance is from the earth to the moon then 1 % is 2,400 miles.

The speed of expansion is the hubble constant. It's close to 70 km/sec per Mega parsec ( (a parsec is a bit more than 3 light years). So the spacetime to alpha centauri is enlarging at closeish to a cm or so per sec. Not a big % of 38 trillion kms.

Note: Someone should check my decimal points I tend to lose them doing that in my head.

At truly large distances like billions of light years the expansion rate starts to get near to the speed of light. Beyond that are almost certainly a lot more of everything but when the expansion rate is greater then c we can never see it. If you think about it and do the calculations you shouldn't be surprised that the distance is around 13 billion light years.