Whether it’s possible to determine that two stars are the same distance from Earth is irrelevant, because we already know that any differences in the distance of those stars from Earth is negligible. The author’s reasoning is based on the distance of the distant galaxy to Earth, not on the comparative difference in distance from individual stars in that galaxy to Earth.

Not necessary, because “elements” is too specific. We have no reason to think the author believes that the “other characteristics” we can correlate with brightness must involve the “elements each star is burning.” Maybe the author’s referring to characteristics besides elements.

Not necessary, because the argument doesn’t concern stars in “our own galaxy.” It’s about stars in distant galaxies.

Necessary, because if this were not true — if there are NO stars in distant galaxies that have characteristics besides brightness that are detectable from Earth — then we have no basis to believe that we can correlate those other characteristics with the brightness of distant stars. For example, if we can’t tell how large the star is or how fast it’s spinning, then we can’t correlate size or spinning speed with brightness.

Not necessary, because the argument is concerned with what we can do IF two stars in a distant galaxy have a significant difference in apparent brightness. It’s entirely possible that many pairs of stars won’t have any different in apparent brightness; this doesn’t undermine the author’s reasoning, which is just based on the hypothetical situation in which we do see a difference in brightness.