The problem is, the very thing you are using to show His actions are anthropomorphic is anthropomorphic in itself. God does not change in the way man changes. There is no contradiction, God does not change His mind in the manner man does, but that does not mean He doesn't change His mind or repent in a divine manner that pleases Him.Because "I change not, because if I did you would have been destroyed a long time ago" is a definitive statement from God about himself.
Proper scriptural interpretation must observe the law of non contradiction. If those statements did teach that God did change and was not immutable then Malachi 3:6 would be contradicted.
So we know that they are anthropomorphisms. For the infinite to communicate with the finite he must condescend or leave the finite uncomprehending anything at all.
Is "believe and you will be saved" anthropomorphic as salvation occurs as a result of belief?