Answer: God can and does change His mind, but only if people sincerely repent of their sins and respond by doing what is right. Sometimes He chooses not to punish someone after he has said that he would. Since God is merciful, He responds readily when people, with their whole hearts, repent.
There are several examples in the Bible of God changing his mind or "repenting" of what he planned. Perhaps the most well known change occurred with Nineveh, the capital of the ruthless Assyrian Empire. When Jonah visited the city, he proclaimed repeatedly that in forty days God would overthrow the city (Jonah 3:4).
Unlike the people of Israel, the pagan idolaters of Nineveh immediately started to repent and put on sackcloth in order to humble themselves before God. They proclaimed a fast that even the king endorsed with a royal decree. The king's reason for the fast was the hope that the Lord would forestall the punishment they deserved (Jonah 3:9).
What was the response of God to those in Nineveh who humbled themselves? He saw what they did and decided in his mind to alter his plans. He decided not to destroy the city (Jonah 3:10).
Another case of our Father changing his will is when King Hezekiah was told he would soon die (2Kings 20:1 - 11). The king, upon hearing the news, prayed, wept and repented. His prayer was heard and Isaiah returned to him with news that he would be healed and granted another fifteen years of life! This example shows that we should pray even when a case seems hopeless since God can certainly change what he intended on doing!
A third, rather striking example of a decision being reversed concerns King Ahab of Israel. Ahab was the worse king who ruled ancient Israel. A prophet no less than Elijah was sent to the king to warn him to repent along with the dire consequences for not doing so (1Kings 16:30 - 33, 21:25).
Ahab, after he could not buy a vineyard next to his palace, whined to his wife Jezebel about it. She arranged for the owner (Naboth) to be put to death through false witnesses who accused him of blasphemy. After Naboth died God sent Elijah to the king as he was in the vineyard making it his own. Ahab was told that the punishment for his many sins would be great evil befalling him and his house (1Kings 21:19, 21 - 22)!
After Ahab heard Elijah warning he did something unusual that caused God to change his mind. The king took off his royal clothes, put on sackcloth, and mourned his sins (1Kings 21:27 - 29). His actions were seen from heaven and the evil God intended was altered to not come upon him personally.
This shows that even a notoriously wicked king can get God to change his mind. There are, of course, other examples of decisions being reversed. Although the Creator knows everything, he sometimes decides to alter his decisions IF people think and act differently in response to his warnings.