To say that Mary is holy is truly a reference back to the earlier statement of "full of grace". God chooses to make holy that which He wills to be so, and by filling Mary with Grace, when was made thus. 

This also is a reference to Mary's being in heaven, for all which is in heaven, is holy, and if we are to believe that Mary is in heaven, then we also should believe Mary to be holy! 

Saying that Mary is the mother of God is actually more a statement of Jesus than it is Mary, for by saying she is the mother of God, we acknowledge the dual nature of Christ: fully God, fully man. By denying that Mary is the mother of God, we deny that Jesus is God, for mother means the person who gave birth to, and the Gospel clearly tells us that Mary gave birth to Jesus! We as Christians acknowledge that Jesus' human and divine natures are inseparable. 

Simply put, Mary is the mother of Jesus, who is God, and so, she is the mother of God!