John 20:19-23 (NAB) Jesus sends his disciples (making them apostles) breathes on them, says receive the Holy Spirit then says who's sins you forgive are forgiven and who's sins you retain are retained.

The question then is, how would the apostle know which sins to forgive and which ones to retain? Unless the repentant sinner told the Apostle which sins he had committed the apostle could not determine the nature of the sinners sins and what to do about them. The next question should be, which sins would an apostle retain and for what reason? Generally if a confessee sins at will week after week and attempts to receive absolution the confessor would quickly determine the insincerity of the sinner. The presbyter would then deny forgiveness or "retain" the sin. It is always God who searches our hearts and responds to our true intentions therefore we can't "trick" God into anything. If the priest gets it wrong he in no way forces God's will.

My question is does the Catholic Church hold that God forgives every crime by confession alone?

Understood as: My question is does the Catholic Church hold that God forgives every sin by confession alone?

A. No! The Catholic Church teaches that Christ instituted the seven sacraments of the new law. Of those seven, three, Baptism, Penance/Reconciliation, and Anointing of the Sick, effect the forgiveness of sin.

The Sacrament of Baptism

For the forgiveness of sins, CCC 1263 By Baptism all sins are forgiven, original sin and all personal sins, as well as all punishment for sin.^{[cf. Council of Florence (1439): DS 1316.]} In those who have been reborn nothing remains that would impede their entry into the Kingdom of God, neither Adam's sin, nor personal sin, nor the consequences of sin, the gravest of which is separation from God.

The Sacrament of Penance/Reconciliation

Please see CCC, II WHY A SACRAMENT OF RECONCILIATION AFTER BAPTISM?

And the Sacrament of the Anointing of the Sick

One effect of the celebration of the Anointing of the Sick CCC 1520 A particular gift of the Holy Spirit. The first grace of this sacrament is one of strengthening, peace and courage to overcome the difficulties that go with the condition of serious illness or the frailty of old age. This grace is a gift of the Holy Spirit, who renews trust and faith in God and strengthens against the temptations of the evil one, the temptation to discouragement and anguish in the face of death.^{[cf. Heb 2:15.]} This assistance from the Lord by the power of his Spirit is meant to lead the sick person to healing of the soul, but also of the body if such is God's will.^{[cf. Council of Florence (1439): DS 1325.]} Furthermore, "if he has committed sins, he will be forgiven."^{[Jas 5:15; cf. Council of Trent (1551): DS 1717.]}

Therefore these are the ordinary ways, established by his Christ, that God forgives sins via the effects of these sacraments.

Can God forgive 'extraordinarily'? Yes!

God has bound salvation to the sacrament of Baptism, but he himself is not bound by his sacraments. cf. CCC, 1257.

Any Biblical reference to the sacrament of Penance? Yes!

A. cf. Article 10 of Apostle's Creed, Penny Catechism 111
What do you mean by 'the forgiveness of sins'?
By 'the forgiveness of sins' I mean that Christ has left the power of forgiving sins to the Pastors of his Church. Jn 20:23.

The reasonableness of Confession

How many are the souls, in distress, anxiety or loneliness, whose one need is to find a being to whom they can pour out their feelings unheard by the world? Tell them out they must; they cannot tell them out to those whom they see every hour. They want to tell them and not to tell them; and they want to tell them out, yet be as if they be not told; they wish to tell them out to one strong enough to bear them, yet not too strong to despise them; they wish to tell them to one who can at once advise and can sympathize with them; they wish to relieve themselves of a load, to gain a solace. If there is a heavenly idea in the Catholic Church, looking at it simply as an idea, surely, next after the Blessed Sacrament, Confession is such. - There is a constant invitation to repent and begin afresh. Prepos. 351 | The Mind of [Bl.] Cardinal Newman| Compiled by Charles Stephen Dessain.

Please note that in Jn 20:23, sins can be retained. For example, the ministers of the sacraments, can judge and make a determination not to administer the above sacraments because of some hindrance on the part of the recipient. cf. CCC, VII. THE ACTS [required] OF THE PENITENT in the Sacrament of Penance/Reconciliation.

So what is actually the relation between forgiving and confessing?

Scriptural answer cf. 1 Jn 1:9 (RSVCE)

9 If we confess our sins, he is faithful and just, and will forgive our sins and cleanse us from all unrighteousness.

Endnote

Please note that one of the fruits of Holy Communion is it wipes away venial sins. [cf. CCC, 1394.]

No; the Catholic Church does not believe that confession by itself is sufficient to ensure forgiveness of sins.

The Catholic Church believes that God alone forgives sins, but has delegated that authority to certain human beings within the Church (cf. John 20:21-23).

God is "gracious and merciful, slow to anger and abounding in mercy" (see Psalm 145); he is also "abounding in steadfast love, and relenting in punishment" (cf. Joel 2:13). Nevertheless, there are three conditions which (except in extraordinary circumstances) the Church believes are required to ensure forgiveness of one's serious sins: confession, contrition, and satisfaction (or penance).

"Penance requires... the sinner to endure all things willingly, be contrite of heart, confess with the lips, and practice complete humility and fruitful satisfaction."

(Catechism of the Catholic Church, paragraph 1450; quoting the Roman Catechism)

Let's take these one at a time.

Confession

This is the practice of telling the priest the sins you have committed since your last Confession. Catholics are required to go to Confession at least once a year; more often is better (and makes it easier to remember what sins you've committed!).

Confession should be preceded by an examination of conscience, in which one thoroughly and frankly looks at one's behavior—one's thoughts, words, and deeds—in light of Christ's commandments. Any serious sins that you remember must be confessed. If after a sincere examination you forget a serious sin (and, for example, remember it only after confession), there is no need to worry about whether you are forgiven—but if you deliberately leave out a serious sin, you are lying (by omission) not only to the priest but to the Lord. This is itself a serious sin. It appears that such an omission invalidates the entire confession; at least that's my understanding of a statement given by the Council of Trent, and quoted in paragraph 1456 of the Catechism:

When Christ’s faithful strive to confess all the sins that they can remember, they undoubtedly place all of them before the divine mercy for pardon. But those who fail to do so and knowingly withhold some, place nothing before the divine goodness for remission through the mediation of the priest, "for if the sick person is too ashamed to show his wound to the doctor, the medicine cannot heal what it does not know."

Contrition

The Catholic Church has a very specific understanding of contrition, and the Council of Trent developed a valuable distinction between what it called perfect contrition and what it called imperfect contrition or attrition; but essentially, contrition is an intense, sincere sorrow for—perhaps even a hatred of—one's own sinful behavior, together with a sincere resolution to avoid sin again.

This, it seems, addresses the problem you bring up. If someone sins Monday through Saturday, and goes to Confession Sunday with sincere sorrow and the sincere intent not to sin again, he's all good, even if he does in fact sin again on Monday. But if he goes to Confession not caring whether he sins on Monday (or perhaps even planning to), he is not showing a desire to be reconciled with God; he does not turn again toward God, and we cannot say that he is forgiven.

Satisfaction (Penance)

Many sins wrong our neighbor. One must do what is possible in order to repair the harm (e.g., return stolen goods, restore the reputation of someone slandered, pay compensation for injuries). Simple justice requires as much. But sin also injures and weakens the sinner himself, as well as his relationships with God and neighbor. Absolution takes away sin, but it does not remedy all the disorders sin has caused. Raised up from sin, the sinner must still recover his full spiritual health by doing something more to make amends for the sin: he must "make satisfaction for" or "expiate" his sins. This satisfaction is also called "penance."

(Catechism, paragraph 1459)

Penance, or satisfaction, involves spiritual and temporal works designed to restore relationships broken and damaged by sin. The Catechism says that penance

can consist of prayer, an offering, works of mercy, service of neighbor, voluntary self-denial, sacrifices, and above all the patient acceptance of the cross we must bear. Such penances help configure us to Christ, who alone expiated our sins once for all. They allow us to become co-heirs with the risen Christ, "provided we suffer with him."

The satisfaction that we make for our sins, however, is not so much ours as though it were not done through Jesus Christ. We who can do nothing ourselves, as if just by ourselves, can do all things with the cooperation of "him who strengthens" us. Thus man has nothing of which to boast, but all our boasting is in Christ... in whom we make satisfaction by bringing forth "fruits that befit repentance." These fruits have their efficacy from him, by him they are offered to the Father, and through him they are accepted by the Father.

(paragraph 1460; the quoted material is from the Council of Trent.)

As the Catechism says elsewhere, God is not bound by his sacraments, and He can forgive even outside the context given here; but this is what the Church believes to be required, under ordinary circumstances, to ensure that sins are forgiven. The simple act of telling one's sins to a priest and having the priest recite the formula of absolution¹ will not do.

¹Here, if you are interested, is the formula:

God, the Father of mercies,
through the death and resurrection of his Son
has reconciled the world to himself
and sent the Holy Spirit among us for the forgiveness of sins;
through the ministry of the Church
may God give you pardon and peace,
and I absolve you from your sins
in the name of the Father,
and of the Son,
and of the Holy Spirit.