Complexity is orthogonal to entropy. The aforementioned barrier-separated box is high in entropy but simple. Upon lifting the barrier, a description of the gas front moving into the vacuum is enormously complex. It is also lower in entropy than the previous, barrier-separated state. Finally, when the gas is diffuse and entropy at its maximum, complexity dips back down.
Life is complex. Plants turn solar radiation into complex living structures; they also diffuse waste heat. Animals eat those plants, make more complex stuff, and generate more diffuse waste heat.
> The aforementioned barrier-separated box is high in entropy but simple.
This isn't true in any meaningful objective sense; representing the exact state of the system in some basis (e.g. the position or momentum states of all particles in the system) requires a huge amount of information, corresponding to the entropy. The GP only said it's a "simple" system because we (for arbitrary reasons) don't really care very much about the position of each gas molecule. We as humans are satisfied with describing the system in terms of bulk statistical characteristics like temperature and pressure. However, we would be unsatisfied doing the same thing with a similarly information-rich system such as a microprocessor, because now the bulk characteristics of the system aren't sufficient information to describe the characteristics that humans care about.
"Simplicity" or "complexity" as described by the GP is not a physical quantity; it's a reflection of which precise dynamical behavior we happen to care about. You could probably find all sorts of heuristics that generally match with human intuition, but in the end it's up to opinion.
As we know, the living stance can be maintained for only a relatively short time, after which it rapidly decomposes to background entropy.
Interesting to speculate, as living beings we are chock full of "micro-environments", there could be exceptions to the laws of nature as we've understood them that could account for certain mysteries of biological nature.
A living organism also increases the entropy of the environment.
Yes, but that's not what the person you replied to was saying. They were pointing out that there can be a global, absolute decrease in entropy, it's just statistically very unlikely.