How were the old saints justified under the law? (Catholic and Protestant views) How were the old saints like Moses and the prophets justified under the law? Were they justified by keeping the law? What is an overview of Catholic and Protestant views on this? Explain with Biblical references. 

This question concerns the technical aspect of salvation that is justification or being right with God. The ability of Mosaic law to give life, and the ability of old saints to obey the law.
Revelation 13:8 says:


  The Lamb who was slain from the foundation of the world.


It seems that God viewed the cross as an event beyond space and time.

If we read Hebrews 9:12-15, we can see and link together the three "eternals". The Lord accomplished an eternal redemption. By offering up Himself to God through the eternal Spirit, we have obtained an eternal inheritance. 

It seems that the redemption of Christ has the divine eternal nature through the Spirit to transcend time in redeeming those who were thousands of years before Him as well as those who are thousands of years after Him. In other words, even if the world goes on for millions of years, Christ's redemption is still effective.

Watchman Nee, in his book, Fact, Faith, and Experience, says:


  If the blood of bulls and goats was not able to remove sin, as we
  mentioned earlier, how then were those in the Old Testament saved? It
  was by the cross. Man had sinned. Hence, only a man could accomplish
  the redemption of sin. Although the animals were innocent, and
  although they were without blemish, they could not redeem man from his
  sins. Why then did God promise in Leviticus 17 that the blood of
  creatures was able to redeem one from sin? There must be some very
  profound meaning here. The things of the law "are a shadow of the
  things to come, but the body is of Christ" (Col. 2:17). Hence, the
  sacrifices and the offerings in the Old Testament all refer to Christ.
  Although Christ had not yet died at the time of the first covenant,
  God intended that all the sacrifices offered at that time be a type of
  Christ. Their death was taken as the death of Christ. Through the
  blood of many animals, God saw the blood of His beloved Son. Through
  many bulls and goats, He saw "the Lamb of God." Through the many
  sacrifices, He saw the substitutional death of Christ. When He
  accepted those offerings, it was as if He was accepting the merit of
  the death of His Son. Because of this, man was redeemed from his sins.
  God reckoned the innocent bulls and goats as His dear Son. Hence, He
  could forgive the sinners based upon the sacrifices they offered.
  Every time the offerings were slaughtered, they spoke of the coming
  sacrifice of the Son of God as the sin offering on Golgotha and of His
  accomplishment of the eternal work of salvation. Because the Lord is a
  man, He is able to redeem man from sin. Because He is God, He is able
  to redeem all men, past and present, from their sins.
  
  Those who offered the sacrifices in the Old Testament, consciously or
  unconsciously, believed in a coming crucified Savior.