"Nothing is supposed to <something>" is a meaningless assertion for entropy. Entropy doesn't suppose things. "Suppose to" implies intent.
Also, entropy might not be directly related to the biological process of aging. I mean, that's the point of TFA.
Indeed exactly this. No system persists or could persist
We're not discussing geological or cosmic eras, just shorter biological processes. Systems can persist for enormous (but still human bound) periods of time.