I hope you don't make your living based on logic, unless you are a lawyer.
Because it was heading toward the light source the entire light spectrum is blue shifted. The wavelength of light absorbed by the atom doesn't change. (Time independent). As long as the framework is maintained, time changes nothing about HOW events occur, it does affect how often.
You are wrong. Change the flow of time, and you most definitely DO change the frequency and the wavelength.
The movement of the atom in the direction of the source does not change the frequency it will absorb.
Yes it will. The Doppler effect applies to both emission and absorption.
Time can change how often an atom does something, especially something time driven like radioactive decay. But it doesn't affect the product of that decay.
It most definitely does. A decay product such as a gamma ray has a frequency. That frequency acts as a clock. If time changes, the clock changes. So you're completely wrong.
Now if the source was moving either towards or away from the (Fixed) atom, its absorption band would still be the same frequency, but it would shift relative to the other spectral lines from the source because the light source is moving and introducing Doppler shifts.
I've told you multiple times now: the source doesn't HAVE spectral lines. The source is broadband. That's why blue shifting the source doesn't matter.
You came here with a theory which you haven't even fleshed out, but which (if true) would overturn an incredibly well tested theory central to modern physics. Your theory is based on nothing other than a hunch, and depend on numbers which are nothing but an unjustified coincidence. It was clear from the start that you didn't understand even rudimentary physics, so it was never credible that you were going to stumble upon a revolutionary theory by accident. Nonetheless, I played along, because hey, you might learn something. You were clueless, but you still seemed to be approaching the topic in good faith.
Your theory has now been disproven. This comes as no surprise to anyone. But this is where your good faith has evaporated. Instead of learning where you went wrong, or trying to discover why the Lyman alpha forest disproves your theory, you have responded with ad hominem attacks. Despite your monumental ignorance of the topic, it appears that you simply never even contemplated the possibility that you needed to learn something new. You have, in short, become the poster child for the Dunning-Kruger effect. So I'm no longer interested in holding your hand as I walk you through where you went wrong. You aren't interested in learning, so the effort would be wasted. If I respond to smack down your nonsense in the future, it will not be for your benefit, but for any lurkers who, unlike you, might actually like to learn.