rcglinsk, if memory serves correctly, we've discussed something like this before, haven't we?

The extreme digest version (well, one such version) goes something like this:

Why is cosmology a science? Because astrophysics is a science.

Why is astrophysics a science? Because physics is a science.

Why is physics a science? So, this discussion is, fundamentally, about what 'science' is (in the last century or three)?

Perhaps if you could distill your questions into these key aspects?

* where do you see the biggest disconnect between cosmology and astrophysics?

* ditto, between astrophysics and physics?

* ditto, wrt your view of science and that you infer from what you read?
To take just one of your specific questions, than can be answered within the framework of the relevant part of science ...

As Ken G and RegisteredUserName have already noted, 'distance' in cosmology (and astrophysics) is something that differs from the vague, absolute idea many of us form from our intuition.

This HTML version of a short paper may be quite illuminating and informative wrt 'distance' (has more meat than the wikipedia page RUN cited): Distance Measures in Cosmology

Concerning the primordial abundance of the light nuclides (1H, 2H, 3He, 4He, 7Li). Detailed studies of BBN (Big Bang Nucleosynthesis) make testable predictions about the abundance of these, relative to the number of 'relict' photons (in the CMB), at the time nucleosynthesis stopped. No surprise that astronomers have done a great deal of research on estimating these abundances! Several have been estimated using at least two independent techniques. And the results are consistent with LCDM models.

If you get a chance, I think time spent reading up on this would be well spent ... how astonishing is it that a model (LCDM) with but a handful of free parameters can not only account for all the billions of datapoints concerning the CMB, but also produce consistent estimates of the abundances of the these nuclides ... throughout the observable universe!

There is one fly in the ointment: the Li abundances estimated don't match those predicted, within the relevant error bars. YMMV, but I think this is saying more about the way the primordial 7Li abundance is estimated, from the various observations, than pointing to a hole in the LCDM models (the nuclear cross-sections are very tightly constrained, so essentially no room to move there). It's a fascinating story; for example, this is the only isotope for which there are three 'creation' processes at work: BBN, stellar nucleosynthesis, and via cosmic ray collisions ('spallation') (there are also, of course, 'destruction' processes at work). So the observed, contemporary, abundance of 7Li is the result of all three creation (and destruction) processes at work over ~13 billion years ... and the corollary is that to estimate the primordial abundance, you need to model these over the history of the universe since the end of the time of BBN. That's tricky.