At the Feast of Booths in Jerusalem people some people thought Jesus was the Christ. Others did not believe, why did they doubt Jesus?

The people knew Jesus was from Nazarath. The Christ was supposed to be born in Bethlehem. They did not realize that Jesus was born in Bethlehem. It is ironic that nobody asked Mary about this.

Source: John 7:41-43

Why did Joseph and Mary go to Bethlehem from Nazareth?

They went to Bethlehem to be counted in the census. Joseph being a descendant of King David who was from Bethlehem.

Source: Luke 2:1-7

Which prophet foretold that Bethlehem would be the birthplace of Jesus?

Jesus birthplace was foretold by the prophet Micah.

Source: Micah 5:2

Which tribe was given Bethlehem when Joshua conquered the promised land?

Bethlehem was given to the tribe of Zebulun by Joshua.

Source: Joshua 19:10-15

What book of the Bible took place around and in Beth-lehem?

The book of Ruth, Elimelech and Naomi were from Bethlehem. After all the males died Naomi and Ruth returned to Bethlehem.

Source: Ruth 1:19 and others