As to your edit, have you read
Trent’s decree on justification? The Catechism talks about it
starting in para. 1987, and the CE also has an article titled
Justification.
You know, funnily enough, I found the part on Justification in the Catechism a few minutes after I posted this topic

Thank you for the links; the part from Trent especially was helpful. That’s a council I’ll be needing to research further, I think.
Also, I’ll post the text of paragraph 1992. Can you please tell me if I have understood it?
Justification has been merited for us by the Passion of Christ who offered himself on the cross as a living victim, holy and pleasing to God, and whose blood has become the instrument of atonement for the sins of all men. Justification is conferred in Baptism, the sacrament of faith. It conforms us to the righteousness of God, who makes us inwardly just by the power of his mercy. Its purpose is the glory of God and of Christ, and the gift of eternal life:
Paragraph 1992
My understanding is that the Catechism is basically using the language of Christ as a sacrifice to God in order to say that He offered Himself up to reconcile us, justifying us (e.g. bringing us out from a state of sin and separation from God, to a state of grace and communion with God, cleansing us of sin and filling us with God’s grace, making us able to further grow in holiness, righteousness, faithfulness, love and charity). Have I understood the teaching of justification correctly?
And likewise, “satisfaction” is the reconciliation between man and God, with us going from being enemies of God to being His friends and sons, and the relationship which was formerly one of estrangement going to being one of communion and love? Is this correct? If not, how?