many scientists have been puzzled by the existence of stars like the Methuselah that appear to be older than the estimated age of our universe
No, not really, because the age of that star is compatible with the age of the universe within the error bars.
These galaxies, existing a mere 300 million years or so after the Big Bang, appear to have a level of maturity and mass typically associated with billions of years of cosmic evolution.
Galaxy formation is still an active area of research und different models predict different evolutionary rates
Instead, he proposes a constant that accounts for the evolution of the coupling constants.
That's exactly what Brans-Dicke theory is trying to do, and other modified theories of gravitation as well. Yet they can't explain stuff so well as Lambda CDM can.
Overall, tired light pretty much doesn't work well explaining the perfect black body behavior of the cosmic microwave background or surface brightnesses of galaxies.