So at what time did time begin? See, time is change.
Time began around 14 billion years ago. I'm not so sure what was so difficult about that question.
So what makes it "outside" our Universe?
Being completely outside of our universe would me to not have any of the same rules apply, and if anything have no rules apply, thus allowing God to be something we are unable to understand outside of the basic concept that he would be omnipotent, omniscient, omnipresent etc.
merely didn't differentiate until later.
Could you explain what you mean by this?
How can God change but not die?
What do you mean by God changing? If you mean in the sense of entropy as you had mentioned earlier, it wouldn't apply to him as none of the universe's properties would apply to him. If anything you could suggest that God is in a vacuum without anything but himself, something definitely beyond us.
We don't say unicorns exist, for example.
I'd say that's a false equivalence, seeing as how, if a Unicorn were to be within our universe many things would apply to it that would rule out it's existence, in comparison to God who would have none of those things apply to it.