Is eternity unchanging?
I don't understand the question. Are you talking about a state of suspended animation? The universe is in a constant state of change/motion.
Is there change in eternity? I guess there must be, since you say God is there waiting for us.
There must be one state of existence in eternity without humans and then at some other “time” (for lack of a better word), be a different state of existence where humans are included in Heaven.
I believe Heaven is eternal and unchanging.
I believe the universe is constantly changing, but I don’t believe that Heaven or eternity is part of the universe. The universe is created.