To the contrary.
God being timeless and immutable are biblical concepts. That the greeks arrived at the truth of what the scriptures tell us about God shouldn't surprise us.
As I alluded to before:
".....that which is known about God is evident within them; for God made it evident to them. For since the creation of the world His invisible attributes, His eternal power and divine nature, have been clearly seen, being understood through what has been made, so that they are without excuse." Romans 1:19&20
My proposed method of systematic theology method is to simply believe what the scriptures clearly tell us and forget greek philosophy, or any other kind of philosophy.
In every way - as the scriptures clearly tell us.
"Jesus Christ (aka God) is the same yesterday, today and forever." Hebrews 13:8
The problem with your rather myopic view conceerning God's changing His mind is that you do not consider that that changing of mind is part of His plan and has been from the beginning.
God's interaction with men is something He has planned to do all along and He has told us so in many places. He has also told us exactly how He will interact in certain circumstances.
One part of God's immutability is His unchangeable nature whereby He will act as He has decreed that He will act in particular circumstances.
No it has not because it is not true.
God knows, always has known, and always will know all things past, present, and future - both possible and actual.
His knowledge is without limits.
Psalm 147:5
"Great is our Lord and abundant in strength; His understanding is
infinite.
Isaiah 40:28
"Do you not know? Have you not heard? The Everlasting God, the LORD, the Creator of the ends of the earth Does not become weary or tired His understanding is
inscrutable.
1 John 3:19&20
"This then is how we know that we belong to the truth, and how we set our hearts at rest in his presence whenever our hearts condemn us. For God is greater than our hearts, and
he knows everything."
Job 37:16 "Do you know how the clouds hang poised, those wonders of him who is
perfect in knowledge?"
Isaiah 46:9&10
"Remember the former things, those of long ago; I am God, and there is no other; I am God, and there is none like me. I make known the end from the beginning, from ancient times, what is still to come. I say: My purpose will stand, and I will do all that I please."
If you don't believe what God says - so be it. But it certainly isn't so terribly hard to understand what He has said. It's pretty darn clear if you have spiritual eyes to see and ears to hear.
Again - this is basic systematic theology 101 (i.e. believe all that the scriptures tell you or be branded a fool by Jesus Christ Himself).
""O foolish men and slow of heart to believe in all that the prophets have spoken!" Luke 24:25