Hans Nelsen said:
Since more distant objects are older, and the farthest objects we receive light from are billions of years old, or rather, their light is billions of years old, in what way, or how different would the distant universe be, if we could see the light it generates today? For that matter does light change as it travels extreme distances, or as it "ages?"
In other words, can we confidently assume that distant regions have evolved more or less along the lines of closer regions, or is there any reason to believe the speed of light prevents us from seeing distant developments that could be different from what might be expected?
In principle it is possible for distant regions to have evolved differently. In practice, probably not. At least, on large scales.
The fundamental issue is this: on large scales, the universe is incredibly homogeneous. With reference to this post, this means two things:
1) At the same redshift, all of the large-scale parameters, such as the number of galaxies and amount of matter, are close to constant as long as we're looking on scales larger than about 250 million light years or so.
2) Across different redshifts, the results of those parameters are consistent with what would expect. For instance, the density changes with expansion exactly as we would expect, and nearby galaxies really do look like evolved versions of far-away galaxies (e.g. more heavy elements, less star formation). For the parameters we can simulate effectively, they are all consistent with uniform evolution.
That observed homogeneity suggests a question: if different regions of the universe were to evolve differently, what could induce them to do so? You'd really need some kind of difference between two regions for them to evolve differently over time. And all of our observations strongly suggest that there are no such significant differences to draw on (again, as long as you're looking at large scales). Furthermore, if it were possible for them to evolve differently over time, why wouldn't they have done so already?
So yes, ultimately the fact that we can't observe anything outside of that narrow cone into our past means that we can't be certain that things outside that cone are the same. But the the universe would make very, very little sense if they were different.