Does God Ever Change His Mind?

Why do some believe that prayer can change God's mind? Why did the people desire a king? Why did God give Saul power of his enemies? Why would some say Saul was being obedient? What is the consequence for men who put their confidence in the flesh? How do we see the wickedness of the heart in self-righteousness when excusing their disobedience to God's command? If your heart isn't bowed to the LORD Jesus Christ is it rebellious?
Why did Samuel cry to the LORD all night? Are there any in hell that God loves? Why must we never conclude anything about God that He hasn't revealed in His Word? What does it really mean when it says that God repented? How does God chasten His own with their own thoughts? How is Christ priceless to His own?