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Assuming we are not special, which is a big assumption, we can generalize that every galaxy is moving away from every other galaxy in space. And since The night sky is not full of galaxies in every direction,
I don’t understand this last part. Every time we get a more powerful telescope and train it on an empty part of the sky we find there are galaxies in every direction. They are widely separated, of course, such is the vastness of space, but I don’t think (contrary to some opinions) that we have seen the edge of the universe yet.
I don't exactly know myself. It's the reasoning that led to the death of the steady state universe theory. If the universe was infinite, then by definition matter, space and time would be infinite. So no matter where we look, some light from some galaxy would have reached us already. I don't know how the finite speed of light plays into this though.
