How did God warn the wise men not to go back to Jerusalem?

God warned them in a dream not to go back to King Herod.

Source: Matthew 2:12

In Bethlehem did the wise men (magi) go to the stable to find Jesus?

No the family had moved to a house be then.

Source: Matthew 2:11

The priests and scribes found that Jesus would be born in Bethlehem. How did they know this?

Jesus birthplace was predicted by the prophet Micah.

Source: Micah 5:2 quoted in Matthew 2:6

How did King Herod and Jerusalem react when the wise men asked for the King of the Jews?

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King Herod and all of Jerusalem were troubled by this. Herod was a Roman client King.

Source: Matthew 2:3

Where did the wise men (magi) go when they were looking for Jesus?

They first went to Jerusalem because they were expecting to find a King.

Source: Matthew 2:1