May a priest later repeat something he has learned in confession?
No. Under no circumstances. The secrecy of the confessional is absolute. Any priest who would tell another person something he had learned in the confessional would be excommunicated. Even to the police, the priest cannot say or suggest anything.
There is hardly anything that priests take more seriously than the seal of the confessional. There are priests who have suffered torture for it and have gone to their deaths. Therefore, you can speak candidly and unreservedly to a priest and confide in him with great peace of mind, because his only job at that moment is to be entirely "the ear of God".
What are the positive effects of confession?
Confession reconciles the sinner with God and the Church.
The second after absolution is like a shower after playing sports, like the fresh air after a summer storm, like waking up on a sunlit summer morning, like the weightlessness of a diver ... . Everything is contained in the word "reconciliation" (from a Latin verb meaning "to bring back together, to restore"): we are at peace with God again. (YOUCAT questions 238 & 239)
Dig Deeper: CCC section (1467-1470) and other references here.
Part 2: The Celebration of the Christian Mystery (1066 - 1690)
Section 2: The Seven Sacraments of the Church (1210 - 1690)
Chapter 2: The Sacraments of Healing (1420 - 1532)
Article 4: The Sacrament of Penance and Reconciliation (1422 - 1498)
VIII. THE MINISTER OF THIS SACRAMENT ⇡
Given the delicacy and greatness of this ministry and the respect due to persons, the Church declares that every priest who hears confessions is bound under very severe penalties to keep absolute secrecy regarding the sins that his penitents have confessed to him. He can make no use of knowledge that confession gives him about penitents' lives.72 This secret, which admits of no exceptions, is called the "sacramental seal," because what the penitent has made known to the priest remains "sealed" by the sacrament.
72.
Cf. CIC, can. 1388 § 1; CCEO, can. 1456.
IX. THE EFFECTS OF THIS SACRAMENT ⇡
"The whole power of the sacrament of Penance consists in restoring us to God's grace and joining us with him in an intimate friendship."73 Reconciliation with God is thus the purpose and effect of this sacrament. For those who receive the sacrament of Penance with contrite heart and religious disposition, reconciliation "is usually followed by peace and serenity of conscience with strong spiritual consolation."74 Indeed the sacrament of Reconciliation with God brings about a true "spiritual resurrection," restoration of the dignity and blessings of the life of the children of God, of which the most precious is friendship with God.75
73.
Roman Catechism, II,V,18.
74.
Council of Trent (1551): DS 1674.
75.
Cf. Lk 15:32.
This sacrament reconciles us with the Church. Sin damages or even breaks fraternal communion. The sacrament of Penance repairs or restores it. In this sense it does not simply heal the one restored to ecclesial communion, but has also a revitalizing effect on the life of the Church which suffered from the sin of one of her members.76 Re-established or strengthened in the communion of saints, the sinner is made stronger by the exchange of spiritual goods among all the living members of the Body of Christ, whether still on pilgrimage or already in the heavenly homeland:77 It must be recalled that ... this reconciliation with God leads, as it were, to other reconciliations, which repair the other breaches caused by sin. The forgiven penitent is reconciled with himself in his inmost being, where he regains his innermost truth. He is reconciled with his brethren whom he has in some way offended and wounded. He is reconciled with the Church. He is reconciled with all creation.78
76.
Cf. 1 Cor 12:26.
77.
Cf. LG 48-50.
78.
John Paul II, RP 31,5.
In this sacrament, the sinner, placing himself before the merciful judgment of God, anticipates in a certain way the judgment to which he will be subjected at the end of his earthly life. For it is now, in this life, that we are offered the choice between life and death, and it is only by the road of conversion that we can enter the Kingdom, from which one is excluded by grave sin.79 In converting to Christ through penance and faith, the sinner passes from death to life and "does not come into judgment."80
79.
Cf. 1 Cor 5:11; Gal 5:19-21; Rev 22:15.
80.