The Hail Mary and Scripture

The Hail Mary (Basic Catholic Prayer):
Hail Mary,
Full of Grace,
The Lord is with thee.
Blessed art thou among women,
and blessed is the fruit
of thy womb, Jesus.
Holy Mary,
Mother of God,
pray for us sinners now,
and at the hour of death.
Amen.

What do you think of the Hail Mary?
Is the Hail Mary a good prayer?
Is the Hail Mary scriptural?

Scripture (RSV-Catholic):
* In the sixth month the angel Gabriel was sent from God to a city of Galilee named Nazareth, to a virgin betrothed to a man whose name was Joseph, of the house of David; and the virgin's name was Mary. And he came to her and said, "Hail, full of grace, the Lord is with you!" - Luke 1: 26-28

If Gabriel "was sent from God", did God send that message?
Did God know Gabriel would say that?
Did Gabriel say that against God's will?
Knowing Gabriel would say that, should God have not sent Gabriel?
Should Gabriel have not said that?

* And when Elizabeth heard the greeting of Mary, the babe leaped in her womb; and Elizabeth was filled with the Holy Spirit and she exclaimed with a loud cry, "Blessed are you among women, and blessed is the fruit of your womb! - Luke 1: 41-42

Is there a relationship between Elizabeth being "filled with the Holy Spirit" and what she said?
Should she have not said that?
Did the Holy Spirit make a mistake?

* And why is this granted me, that the mother of my Lord should come to me? - Luke 1: 43

Is there a relationship between Elizabeth being "filled with the Holy Spirit" and what she said?
Should she have not said that?
Did the Holy Spirit make a mistake?

* and Simeon blessed them and said to Mary his mother, "Behold, this child is set for the fall and rising of many in Israel, and for a sign that is spoken against (and a sword will pierce through your own soul also), that thoughts out of many hearts may be revealed." - Luke 2: 34-35

Should Simeon not have said that?
Was Simeon wrong?

Is the Bible true?

pax tecum