On the first item, what is your explanation for the uniform expansion of the universe, and of the cosmic microwave background? On the second, how do you explain gravitational lensing, and what do you think happens to the relativisitic field equations at very high matter densities?
I'm not certain that there is any expansion. BB was introduced to explain why there is an expansion. But BB cannot account for galactic clusters, super clusters, or even star clusters. In the BB universe, star clusters cannot have formed because it takes more years to form them than the universe has existed. Even worse for galactic clusters. Even worse for the super clusters that have been mapped. BB originally assumed a homogenous starting point. The observed universe is too 'lumpy' for observation to agree with BB. So BB was modified to have small lumps in it in the first millionths of a second after the bang (or some tiny time frame.) Now the BBers want to use the uniformity of the microwave background as evidence of BB. Did you catch the fallacy there? The universe is NOT uniform, but the uniformity of the microwave radiation is used as evidence of the BB.
First, the universe sprang from a singularity but the universe is too lumpy for that.
So they changed it to the universe sprang from "quantum quasi-singularity thingy" to account for the lumpiness but try to use the uniformity of the microwave radiation as evidence that a NON-uniform thingy grew into the universe.
Then there were all the failures in the prediction of the elements. I believe namely the ratio of hydrogen, helium, and deuterium. If I remember correctly, it was "inflation" that was invented to account for the discrepancy between observation and prediction.
As to what I think "happens to the relativistic field equations at very high matter desities?" -- The question is flawed. It asks what I think about an equation when some part of it is "high". The real question is "does relativistic field equations correctly predict what is observable in objects with extremely high densities?"