The universe is only expanding according to the doppler interpretation of redshift, but Halton Arp showed this interpretation to be flawed.
Actually the steady state model was much more accurate with its prediction.
Obviously if the radiation gets red-shifted it cools down. That is no argument for the BB.
That is completely false. The galaxies at the very edges of the visible universe look EXACTLY the same as those in the very center. The problem is that in a Universe of a mere 15 billion years (only three times as old as the minimum age of the infinitesimal earth) those furthest seen galaxies would have only rotated about two times!! That is simply not enough time to create the spiral structure that they exhibit.
Plasma Cosmology can deal with that as well through fusion and fission processes in stars. See www.electric-cosmos.org
if you care to understand the alternatives which you are dismissing off-hand.