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"Why the need for a new covenant, if God doesn’t change His mind? Jeremiah 31:31-34

This is not a example of G-d changing his mind. This is a prophecy of what is to occur when Israel returns in the Messianic era. Israel had blown it and were sent into exile. So, now when Israel returns, they will resume the commandments and sacrifices will return in the 3rd temple. Furthermore, G-d is not changing his salvation plan in this "new covenant".

And I shall give them one heart, and shall put a new spirit within them. And I shall take the heart of stone out of their flesh and give them a heart of flesh, that they may walk in My statutes and keep My ordinances, and do them. Then they will be My people, and I shall be their God. (Ezekiel 11:19-20)

And many peoples shall come, and say: "Come, let us go up to the mountain of the Lord, to the house of the God of Jacob; that he may teach us his ways and that we may walk in his paths," for out of Zion shall go forth the law, and the word of the Lord from Jerusalem. (Isaiah 2:3)

And what will the Gentile Nations response be to this miracle of the Jews returning to God and following the commandments???

O LORD, my strength, and my fortress, and my refuge in the day of affliction, the Gentiles shall come unto thee from the ends of the earth, and shall say, Surely our fathers have inherited lies, vanity, and things wherein there is no profit.

20Shall a man make gods unto himself, and they are no gods?

21Therefore, behold, I will this once cause them to know, I will cause them to know mine hand and my might; and they shall know that my name is The LORD. (Jeremiah 16:18-21)

23Thus saith the LORD of hosts; In those days it shall come to pass, that ten men shall take hold out of all languages of the nations, even shall take hold of the skirt of him that is a Jew, saying, We will go with you: for we have heard that God is with you. (Zech 8:23)

So, contrary to G-d changing his mind he will keep his word, restore Israel and the Nations will worship the G-d of Israel by learning at the hands of the Jewish people.

"Why didn’t Abraham sacrifice Isaac, if God doesn’t change His mind?

Again, no change of mind. This was the 10th and final trial of Abraham. He had no intention of sacrificing Issac. He wanted to see if Abraham feared G-d. Abraham feared G-d enough to do as he was commanded but Abraham had faith that G-d would provide a animal, which He did. (a Ram not a lamb)

Regarding Noahs flood, if G-d would have changed his mind He would utterly destroyed all of mankind forever. But he saved a remnant, to carry on with. Being sorry isnt the same as changing his mind. Blotting out man forever would have been.