You cannot state that God lives outside of space-time since there is no way for anyone inside space-time to be aware of that.
As for the bat you are arguing out of ignorance when you say it will catch only food and nothing inedible.They will catch things that are inedible and then release them so their powers of analysis are not by way of their echo-location but by sense of taste.I have personally tested this idea before by throwing small pebbles into the air and watching bats catch them.If you do it often enough in a short time they will learn to be more cautious,however you can return the following night and they do not retain the memory and will proceed to repeat their error.
Now as to his existing forever the bible itself has God state a contrary position in Revelations 1:8
"I am Alpha and Omega, the beginning and the ending, saith the Lord, which is, and which was, and which is to come, the Almighty"
Our cosmology models do not point to a beginning from nothing and you have made the same error that is continually brought up in even science texts.You state:
"Since matter exists in this universe and is subject to loss of energy, matter cannot have existed for eternity."
It is not true that matter is subject to loss of energy.We do not even have a definition of what energy is.The only thing we understand is that when we calculate the actions of matter in its motion from one condition to another there is a quantity that remains the same.It is an abstract thing and we have no idea exactly what it is.Our deepest understandings of physics and mathematics do not allow us to understand how the universe actually came into being.However,what we do know is far more subtle than most people realize and God simply doesn't enter into the equations.
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