What are some ways scripture speaks of God's changing? Does this violate his being unchangeable?
God does not change.
Numbers 23:19 God is not a man, that He should lie, Nor a son of man, that He should repent. Has He said, and will He not do? Or has He spoken, and will He not make it good?
Psalm 102:25-27 Of old You laid the foundation of the earth, And the heavens are the work of Your hands. 26 They will perish, but You will endure; Yes, they will all grow old like a garment; Like a cloak You will change them, And they will be changed. 27 But You are the same, And Your years will have no end.
Malachi 3:6 For I am the LORD, I do not change; Therefore you are not consumed, O sons of Jacob.
James 1:17 Every good gift and every perfect gift is from above, and comes down from the Father of lights, with whom there is no variation or shadow of turning.
God, in a way that we do not understand, knows the future in minute detail and has a purpose with the earth which he will not deviate from.
But when God threatens a nation with punishment for their sin and they hear and repent, then he will not bring the punishment upon them.
This is clearly seen in the account of Jonah and Nineveh.
Jonah 3:10 Then God saw their works, that they turned from their evil way; and God relented from the disaster that He had said He would bring upon them, and He did not do it.
Also when God promises a blessing upon a nation if they obey him and they do not obey, then the blessing will not come, it will be replaced by a curse. This is demonstrated in the words of Moses when Israel moved into the promised land:
Deuteronomy 27:1,2 Now it shall come to pass, if you diligently obey the voice of the LORD your God, to observe carefully all His commandments which I command you today, that the LORD your God will set you high above all nations of the earth. 2 And all these blessings shall come upon you and overtake you, because you obey the voice of the LORD your God
Deuteronomy 28:15 But it shall come to pass, if you do not obey the voice of the LORD your God, to observe carefully all His commandments and His statutes which I command you today, that all these curses will come upon you and overtake you
It is because God does not change that we can have the hope of resurrection from the dead to eternal life in the future kingdom of God if we believe and obey the Gospel preached by Jesus and his apostles. Jesus told his apostles:
Matthew 28:19 Go therefore and make disciples of all the nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, 20 teaching them to observe all things that I have commanded you…
Mark 16:15,16 And He said to them, "Go into all the world and preach the gospel to every creature. 16 He who believes and is baptized will be saved; but he who does not believe will be condemned.
God does not change, but we as sons of Adam certainly do need to change.
Ezekiel 18:32 For I have no pleasure in the death of one who dies," says the Lord GOD. "Therefore turn and live!
Romans 6:23 For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord.
I hope you find this helpful.