Seem we have to atone our sins ourselves as per Ezekiel 18?

"if there is someone willing to die for my sins".

Willingness isn't enough. I might be willing to pay off your mortgage and student loans, but I can't because I don't have enough money. Paying your debt of death can't be done by anyone that has sinned, as they have already forfeited their own life and don't have it available to pay your debt.

The only human that didn't sin, and is therefore able to pay your debt, is Jesus. (And his life is worth far more than any one human's life, so he can pay many such debts.)

This is the fundamental concept of Christianity.
Until one properly understands this idea, one can never really understand anything else about Christianity.

First of all, the source:

Ezekiel 18:4 (GNT): The life of every person belongs to me, the life of the parent as well as that of the child. The person who sins is the one who will die.

God states clearly that even if there is someone willing to die for my sins (or settle on my behalf), still not possible due to God's method of settling the issue of sin.

IF this is the case, Jesus die for nothing? His death doesn't settle anything for the wicked...

So, let's be clear that the OP is arguing against the Mosaic Law with its system of atonement via sacrifice of innocent animals. The soul that sins will die. Period, end of discussion. Where does this leave us? Most miserable creatures that we are.

But there is another prophet of God who said this.

Who hath believed our report? and to whom is the arm of the LORD revealed? Isa 53:1

But he [ was wounded for our transgressions, he was bruised for our iniquities: the chastis*m*nt of our peace was upon him; and with his stripes we are healed. Isa 53:5

He shall see of the travail of his soul, and shall be satisfied: by his knowledge shall my righteous servant justify many; for he shall bear their iniquities. Isa 53:11

Messiah was sinless, yet He died as a sin offering. But God was pleased and thus raised Him from the dead and seated Him on high.

The soul that sins shall die. There is One however. We pray all come to repentance.

Ezekiel was written during the Babylonian Exile, when the people of Judah feared there was no hope for them as a nation. Based on teachings such Deuteronomy's warning that God would punish the children "for the sins of the father" through the fourth generation (Deuteronomy 5:9) they had begun to lose hope.

Ezekiel countered the people's hopelessness by declaring in God's name:

What do you mean by repeating this proverb concerning the land of Israel, ‘The fathers have eaten sour grapes, and the children’s teeth are set on edge’? As I live, says the Lord God, this proverb shall no more be used by you in Israel. Behold, all souls are mine; the soul of the father as well as the soul of the son is mine: the soul that sins shall die. (Eze. 18:2-4)

The chapter concludes:

I will judge you, O house of Israel, every one according to his ways, says the Lord God. (18:30)

These verses indeed seem incompatible the idea of Original Sin, which holds all people accountable for the sin of Adam. As Paul wrote:

For as in Adam all die, so also in Christ shall all be made alive. (1 Corinthians 15:22)

Did Jesus Die for Nothing?

Does this mean, as the OP asks, "did Jesus die for nothing?" Not according to Christian doctrine. Christians simply have to accept the fact in Ezekiel's time, the teaching of Original Sin had not yet been revealed. Ezekiel wrote to counter the people's misunderstanding of God's hope for the Exiles. This is a different problem from the issue that Paul wrote about or that the Catholic Church taught about. Indeed, the formal doctrine of Original Sin would not be fully developed until the time of St. Augustine, who was the first to use the term. Augustine spoke of:

...those who had not sinned after the likeness of Adam’s transgression; that is, who had not yet sinned of their own individual will, as Adam did, but had drawn from him original sin.

The Christian teaching is that Christ indeed died for our sins, both the sins we commit personally and the Original Sin inherited from our first ancestor. Just as Ezekiel's teaching was not based on Deuteronomy's formula, the Christian doctrine is based primarily on the teachings of Paul and Augustine, not on the prophecy of Ezekiel.

You are misquoting the verse to start with. The whole chapter deals with a false perception of that children may safer consequences for their parent's sins. God through Ezekiel explains that everyone is only responsible for his/her own sins. Sins of the parents are not passed onto their children.

A righteous one giving up his life for others is an ancient Jewish concept older than Christianity. Moses offered his life to save Israelites in Exodus 32:32. Then there is Isaiah 53. What is it all about? The righteous one suffering for the sinners.

The whole sacrificial system worked as a picture of a blameless one being a substitute for the sinner.

The text you use as your source certainly shows that death is the result of sin. Building on that source, another text gives further information relevant to that fact. It is in Romans chapter 6, where Christians are told that they have been set free from slavery to sin, the result being holiness, and eternal life.

This, however, does not mean that they avoid physical death because they still were, and still are sinners. The accumulated body of sinful works they did in their life still means that they have to die, because "the soul that sins shall die". Further, the last verse in this chapter adds a vital fact. It is that:

"The wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord." Romans 6:23

Now, a wage is earned, is it not? Work is done, and payment is an obligation; the worker must be paid for the work done. Thus Romans 4:4 confirms that:

"Now when a man works, his wages are not credited to him as a gift, but as an obligation."

That is why God pays every sinner the wage they have earned for the body of sinful works they have built up. They receive death. But nobody can receive their wages then try to hand it back to the one who paid them in order not to receive the wage! That is absurd! God's wage to every sinner is physical death and nobody can refuse to receive it. They must die. They will die. They do die. Ezekiel 18:4 is in perfect harmony with Romans 6:23.

All of this is contrasted with the amazing gift of forgiveness of sins which results in everlasting life, to those who believe. Romans 4:5 adds that to the man who does not work but trusts God who justifies the wicked, his faith is credited as righteousness (then Paul quotes Psalm 32:1,2 and refers to the faith of Abram). This means that sinners must stop working to try to "earn" God's forgiveness because they can only earn death, due to everything they do being polluted with sin. Once they believe that only the finished work of Christ at Golgotha can enable the free gift of forgiveness and everlasting life, they are set free from their slavery to sin. They still receive their wage of physical death, but even before they receive it, they have received God's gift of salvation and step instantly from death to life, the moment they believe.

This explanation shows why nobody can 'atone' for their own sins. Dying is the result of sin and does nothing to remove that sin because death is proof that this body of sinful works has been done.

On the other hand, the only man who never sinned, voluntarily gave himself over to physical death in order to atone for those who would repentantly believe in what he had done. Jesus need never have died, for he had never sinned. But he came to give his perfect life an offering for sin - Romans 8:3. That is why death could not hold him, for death can only claim sinners. Christ arose, triumphant over sin, death and the grave. All who trust in that provision, in faith, are baptized into Christ's death, and raised in newness of life.

You ask if God's method of settling the issue of sin means that Jesus died for nothing? On the contrary, God's method of settling the issue of sin meant that Jesus had to die as the only perfect sacrifice for sin there has ever been because our deaths simply confirm that we are sinners! Only Jesus' death can take away our sins in God's eyes. That is why, when we put our faith in that, the issue of our sin is settled.

I am crucified with Christ [Galatians 2:20 KJV]

says the apostle Paul, who also tells 'all who are in Rome, beloved of God' to :

... reckon ye also yourselves to be dead indeed unto sin, but alive unto God through Jesus Christ our Lord. [Romans 6:11 KJV]

And again, he says ,

... For ye are dead, and your life is hid with Christ in God. [Colossians 3:3 KJV]

'The soul that sinneth, it shall die' said Ezekiel [Ezekiel 18:4 KJV] and that is the case.

Some die outside of Christ. They die because of sin and they perish, unsaved.

But some are dead with Christ, in his death.

By faith, they enter into death, through Christ. Thus are they baptised into his death. Death has no more dominion over them.

When their mortal existence comes to an end (as, in righteousness, it must) then they 'sleep in Jesus' because sin was dealt with already in the death of Jesus Christ.

Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life. For if we have been planted together in the likeness of his death, we shall be also in the likeness of his resurrection: Knowing this, that our old man is crucified with him, that the body of sin might be destroyed, that henceforth we should not serve sin. . . . . . . . . . . . . . . . . For he that is dead is freed from sin.

Romans 6: 4-7 KJV