Final answer:
Living one billion light-years away from the Milky Way, we would observe the universe as it was one billion years in the past due to the way light travels over time. Consequently, we would see the Milky Way and other galaxies in different stages of their evolution. Cosmological observations are subject to uncertainties but would provide valuable insights into the universe's past.
Step-by-step explanation:
If we lived in a galaxy one billion light-years from our own, we'd have a remarkable view of galactic structures and astronomical phenomena different from the sights of our current night sky. Most importantly, we would observe the light emitted from galaxies and stars as they existed one billion years ago since the light-years measure both distance and the time that light takes to travel to us. When we see distant galaxies, we are essentially looking back in time due to the finite speed of light.
Living one billion light-years away, we'd see our galaxy as it was one billion years ago, likely without the well-defined structures we recognize today. We might also witness some galaxies as they were forming, stars in various stages of their life cycles, and the overall evolution of the universe's structure. Globular clusters in this distant galaxy would likely present a starkly different view with densely packed stars appearing as bright points of light in the sky, potentially more vivid than any stars visible from Earth.
In this distant galaxy, the skies would offer insights into cosmological phenomena, such as the distribution of galaxies and their evolutionary states, subject to the caveat that cosmological observations come with great uncertainties.