How do you get from "a closed system, that perpetuates itself, where nothing can be added or subtracted without changing what it is," to an "eternal" system? I would think an eternal system would be the "open" one, practically by definition (for such a system would not be time delimited).
The closed system that you describe need not be eternal. And it wouldn't be, if it had a beginning. And presumably anything that has a beginning has an end also.
But of course, here we are speaking from within the category of time that human beings are accustomed/habituated to by observation and experience — 4D spacetime. What is in eternity — in timelessness — is not "in" 4D spacetime, nor can it ever be a direct perception of the human mind.
So, having said that, why should I find your "cosmology" preferable to the Christian one — which actually takes such temporal distinctions seriously, and makes them explicit?
Because that which is unchanging is eternal.
What is the meaning of open and closed outside this universe?
"What is in eternity — in timelessness — is not "in" 4D spacetime..."
Time exists outside this universe. Otherwise a photon's clock wouldn't work. Nevertheless, one needs that particular dimension for a real instance of an existence.