Most of the people mentioned as ancestors of Jesus were men. But the gospels mention some women as well. Name 3 of the 4 women named as Jesus ancestors?

The list of women listed as ancestors of Jesus are;

1. Tamar
2. Ruth
3. Bathsheba(Listed as Wife of Uriah the Hittite)
4. Rahab(Not the one in Joshua)

Source:

Matthew 1:2-16

Luke traces the ancestry of Jesus all the way back to Adam.  But what Son of Adam was Jesus ancestor?

Luke was a descendant of Seth the third son of Adam and Eve.

Source:

Luke 3:38

Jesus was also the son of God. One prediction is  in the book of Psalms, what Psalm predicted this?

The prediction is in Psalm 2 verse 7.

Source:

Psalm 2:7

Jesus is also a descendant of a famous King of Israel.  What is the King’ s name?

Jesus is indeed a descendant of King David. This is found in the Old Testament in at least  two places.  Also in the gospels

Source:

Isiah 9:7, Jeremiah 23:5, Matthew 1:1, Luke 2:4

Jesus is of the tribe of Judah?  But which patriarch prophesied this for Judah?

Jacob made the prophecy to his sons in Egypt.

Source:

Genesis 49:10