Is the nature of the atonement in terms of sacrifice or renewal?
There are elements of both, I suppose. A sacrifice that brings renewal. To atone is “to reconcile by making amends or compensation” (Glossary in
The Salvation Controversy by James Akin, which by the way may be of interest to you if you want to learn more about this subject). It is by His sacrifice that Christ atones for the sins of mankind, and it is by this atonement that mankind is renewed, made a new creation.
Is the extent of the atonement with regard to the past only or the future as well? In other words, is the atonement for original sin or also for sins thereafter? If the former, does that mean we are no longer born in original sin? If the latter, why are there still mortal sins that must be confessed to have hope for salvation?
Speaking in terms of efficacy at least (see below), it extends to both the Original Sin and personal sins of the elect. That is, all who will go to heaven will be purified of both Original Sin and personal sin by the sacrifice of Christ.
This ordinarily takes place first at baptism, when both Original Sin and, if the neophyte is an adult or older child, any personal sin is forgiven. Baptism does not, however take away the psychological and physical effects of Original Sin, for which reason we continue to tend to fall into sin even after baptism. These later sins are ordinarily forgiven in the Sacrament of Penance (aka Sacrament of Reconciliation or Confession).
In these sacraments, as in the other sacraments in different ways, the Christian is brought into the mysteries of Christ’s life, death, and resurrection. They are the ordinary context in which the Atonement earned by Christ is applied to individuals. Of course, God is not bound by the sacraments He has instituted, and so can theoretically work outside of them, but ultimately all salvation will be through Christ and His Church whether the individual realizes it in life or not.
Even though through divine indwelling we no longer “have” Original Sin, our human nature remains fallen and thus the children even of the baptized are still born with Original Sin.
How does all this differ from Protestantism’s view on the nature and the extent of Jesus’ atonement? And what does Catholicism say about the concept of “limited atonement”?
There is no single Protestant view on Jesus’ atonement. The idea of “limited atonement” is popular, though not universal, among Calvinists, and essentially says that Christ died only for the elect, not for the whole of humanity.
Catholics would take a more nuanced view. On the one hand, God in some sense wills the salvation of everyone, and Christ’s sacrifice was sufficient for the salvation of all human beings; indeed it was
supersuficient. He therefore grants grace sufficient to receive this salvation to all human beings -none will be damned except by their own choice in rejecting this salvation. On the other hand, God has always known that a limited number of human beings (called the
predestined or the
elect) would actually accept the offer of salvation, and in His Divinity Christ knew who these would be and that these alone would actually be saved by His sacrifice. Thus the atonement is limited in its
efficacy but not limited in its
sufficiency.
This two-layered sense of who Christ died for fits well with Paul’s description of Christ as "the Savior of all men, especially those who believe” (1 Timothy 4:10). In terms of God’s universal salvific will and the sufficiency of the sacrifice, Christ is the Savior of all men (men and women). In terms of predestination and the actual working of grace in the individual soul, Christ the savior only of those who freely cooperate with that grace.
Finally, is the atonement by virtue of Jesus’ death only, or also his suffering?
The atonement is due to the entire eternal sacrifice of the incarnate Son to the Father. The nature of that sacrifice from the point of view of Christ’s Divinity is very interesting but very difficult. In terms of His humanity, I have seen the Last Supper and the Agony in the Garden alternatively cited as the starting point of the redemptive sacrifice. I could also easily imagine someone taking the position that it began with His allowing Himself to be taken into custody in the garden. In any event the sacrifice did not cease to be offered with the death of Christ, but continues in an “unbloody” manner unendingly in heaven. It is this unbloody sacrifice, which is the same sacrifice as that of the Cross in that it has the same priest, the same victim, the same purpose, and a sort of continuity with the Cross, that is made present (“re-presented”) at the Mass. Christ’s death is of course a crucially important part of this atoning sacrifice, but the act of sacrifice is not confined to that one moment in time.
As to whether Jesus’ physical and emotional sufferings were an integral part of this atoning sacrifice and are in some way themselves redemptive, certainly the popular piety of Catholics would suggest to me that they are. I’ve honestly never before thought of separating the fact of Christ’s death from the sufferings He endured on the way to that death. In His human nature the actual, historical, finite sufferings Jesus endured were a real part of His total offering of Himself to the Father, so I would view them as very much a part of the atonement.