1. Depends on what one means by a vaccum (Outside in the parking lot? Inside a sealed container cooled to as much as we can cool it on earth?). If there is nothing there, then the Universe is a vacuum. The speed of light doesn't say anything about the idea the phton isn't there (is a geodesic a discontinuous function? Are there gaps in a geodesic?
2. Depends on what one means by a second observer. God? Thee?
3. That's only verifiable if you know all the reference frames.... (suppose there is something you're missing. Does god know about it? And/or can you fill it in with your imagination? (Wheeler's "bits", Susskind's Holographic Universe..
(to leave the center of the light cone, you have to travel faster than light. Sir Arthur Eddington's comment about gravity waves - "Gravity waves travel at the speed of thought...
1. Spectra is an energy measurement, not a space time velocity. So is the Minkowski metric, and the so-called "time dilation" equation.
On the subjective level light travels instantaneously, and doesn't interact with matter (at least when you're sleeping)... Unless you get a sunburn or are trying to shoot down a fast burn booster... (Nevertheless, it is important to keep track of the neutrinos that are striking your body at any given instant..)
2. Hydrogen as measured in our experience on the earth's surface. The situation in the center of Sagittarius may be quite different (, or, hey, inside a semiconductor for that matter ).
3. Olbers' paradox represents on an essential hypothesis of geometric optics and the concept that photon's don't interfere with each other. Some people call such interference spin polarization, some call it gravity, some call it the Force, which you can feel if you close your eyes and bounce up and down cross-legged on your bed.
(IMO) The CBR is just noise produced by photons you can't see between you and wherever else you're looking - you don't observe the photons that don't get to you - even if they are geodesics).
And the farther out you look, the smaller the solid angle, and the more the noisy photon-on-photon interference, so the more energy a photon has lost trying to get to you. With Einstein rings (a geometric optics phenomenon as observed) you only vies the "center's in terms of optical light (with a smidgen of (formerly) "dark" matter (i.e., barely observed light) - which in this context of light is dark energy as unobservable photon spin interactions locally. That's why the metric of the stress-energy tensor is not diagonal for the case of gravity... (but then, the characterization of the Universe is not "complete" as Einstein admitted later on, when he admitted the speed of light had to change for such a description (by analogy to refraction where "space-time) as a medium - that is, interpreted as a mass field. What if there is no mass - what does it mean for light to travel through a space where there is no light if the geodesic is a continuous function and quantum mechanics does not apply (h = 0)?
The philosophical is - If the speed of light is constant on earth (in the parking lot), and it is the only way that we can observe and understand the universe (assuming our brains are quantum limited as calculators), is the Universe a "Ghost in the Maschine" or is it the All-Encompasing Wow? Or are we just noise on the surface of the unit sphere we call earth, or a speck in the stream of consciousness.
It all depends on your religion....
(IMO) Cosmology is a fools' errand, since it posits the existence of some (other) observer before you were born... The Big Bang is what happened just before the gleam in your daddy's eye faded out. The only consciousness that exists are Thee and Me, and I am not altogether sure about Thee...
Science suggests that after the Big Bang, god smoked a cigarette, rolled over, went to sleep, and hasn't been heard from since.
However, the Bibble teaches that he woke up, knocked up a poor carpenter’s fiancÚ, convinced the locals that it was a virgin birth, and then threw his illegitimate son under the bus when he turned out to be a liberal. The locals testified that the son appeared to them after his death, a story that perseveres to this day, often as images on the crusts of toasted cheese sandwiches.
God has strong Republican CEO core values...
And since when do Republican values have anything to do with Christianity?