Which Catholic encyclicals discuss the Catholic teaching on the results of Jesus' sacrifice? Which Catholic papal encyclicals discuss questions like - 

1) Why did Jesus have to die?

2) What are the effects of the sacrifice of Jesus? 

3) How does God look at the world before and after the sacrifice of Jesus? 

If there aren't any papal encyclicals, are there any books / writings that discuss the same?
This is a very broad question, but to answer your question briefly, the Baltimore Catechism says:

Q. 398. Why did Christ suffer and die?
A. Christ suffered and died for our sins.

Q. 453. Which are the chief effects of the Redemption?
A. The chief effects of the Redemption are two: The satisfaction of God’s justice by Christ’s sufferings and death, and the gaining of grace for men.

For your third question, God still considered the created world to be good: "For every creature of God is good." (1 Tim. 4:4a).

An excellent encyclical that covers Christ's sacrifice, its necessity for our redemption and salvation, and its relationship to the Holy Sacrifice of the Mass is Pope Pius XII's 1947 Mediator Dei.