@Herald,
I think you may have a greater knowledge of the terminology on several of these matters than understanding of the ideas behind it.
The entropy of the universe and all systems within it does indeed increase over time, but it is a long way from uniform disorder. The Big Bang theory suggersts that it started with an extremely high level of order with energy concentrated at the singularity. It's still got a long was to go.
We know a lot about the processes attending star formation and eventual destruction in a supernova or contraction to a white (or blue) dwarf state (depending on the initial mass of the star. These are processes that involve the evolving disorder of a mature star and its eventual destreuction, while the formation of a star involves gravitatioonal growth, increasing temperatures and ignition to fusion - a process involving increasing local order and decreasing local entropy. All of this occurs repeatedly in the unfolding evolution of our universe.
Chaos is a scientific term describing something entirely distinct from entropy. Chaos instead involves the sensitivity of the behavior over time of non linear dynamical systems to small variations in their initial conditions, and the uncertainties attendant to any prediction of their future state This is what makes it impossible to create accurate long range weather forecasts using numerical models based on current measured conditions. It has nothing to do with entropy.
That the universe and our solar system are evolving is undeniable. Our sun formed about 4.5 billion years ago and it will end its life (and that of the earth) as a red giant in the distant future. That, of course assumes that the earth won't first collide with Venus or Jupiter in a chaotic unravelling of the planetary orbits in our solar system induced by some wandering asteroid.
You overrate the hazards of nuclear radiation. Your body is naturally radioactive, and you live your life bathed in radiation from the sun and naturally occurring radiation from the earth. Moreover common choices affect the levels of that radiation far more than you may realize. If you were to move to (say) Vail Colorado you would be accepting an increase in the natural radiation dose that is several times the legal limit for a worker in a nuclear power plant. Indeed that is true for most cities at high altitude. The public health data doesn't show any effect (except that mortality for a cigar smoking boozer from Las Vegas is a good higher than that of a non-smoking tea totaler from Salt Lake City.
The ancients did indeed produce some fairly accurate star maps. That however doen't mean they understood the reality of the motions of the heavenly objeccts they plotted. That is very obviously what i was referring to. I think you are just throwing stuff out there to see if it sticks.