Question: "Where do we find any evidence that praying for the dead is a biblical? From what I have read it appears that the Bible almost says the opposite of this in Ezekiel Chapter 18. Sure, Ezekiel was talking to Israel prior to the New Covenant that we have in Christ, but it says at the start of the chapter that this came from the word of the LORD and it seems consistent with Romans 2:3-9."
What does the Bible Say?
First, let me point out that neither of the passages cited address the question of praying for the dead.
The point of Ezekiel 18 is that a son is neither saved nor condemned because of the righteousness or the sins of his father, and neither is a father saved or condemned because of his son. Also, past righteous will not save a man who falls into sin, nor will past sin condemn a man who turns from his sin. The passage is not about prayers for the dead.
The point of Romans 2:3-9 is that everyone will be judged according to his works, This has nothing to do with prayers for the dead either, unless you assume that we believe that by praying for the dead we could pray an impenitent sinner into heaven, but we do not believe that.
There are, however, passages of Scripture that do address this question. 2nd Maccabees is not in most Protestant Bibles, but it was included in the 1611 King James Bible, and has been considered to be part of Scripture by the Church since the time of the Apostles (see Canon 85 of the Holy Apostles) -- and in 2nd Maccabees 12:38-45 we find a very clear example of prayer for the dead.
In the Wisdom of Sirach (which is also listed among Scripture by the Canon 85 of the Apostles), it says: "Give graciously to all the living; do not withhold kindness even from the dead" (Sirach 7:33).
And in 2 Timothy 1:16-18, St. Paul is praying for Onesiphorus, who obviously is no longer among the living:
"The Lord grant mercy to the household of Onesiphorus, for he often refreshed me, and was not ashamed of my chain; but when he arrived in Rome, he sought me out very zealously and found me. The Lord grant to him that he may find mercy from the Lord in that Day—and you know very well how many ways he ministered to me at Ephesus."
The text from Second Maccabees that has already been cited is clear evidence that this was the Jewish custom well before the time of Christ, but is also a fact that the Jews continue to pray for the dead. So if prayers for the dead were some pagan corruption that crept into the Church, one has to wonder how it also crept into Judaism... especially when this would have to have happened before the the time of Christ.
When I first began to seriously consider becoming Orthodox, prayers for the dead were on my list of about 5 issues that had to be resolved, but it was also one of the first issues to be scratched off that list, because the evidence that the early Church prayed for the dead is far too ubiquitous to allow one to doubt it. You find it in the earliest texts of the Liturgy. You find it passing comments made by the earliest writers of the Church. You also find them in the catacombs. For example, we have the Epitaph of Abercius, Bishop of Hieropolis, who reposed in 167 A.D., in which he asks for those who read the epitaph to pray for him. When St. Augustine's pious mother was departing this life, her last request was: "Lay this body anywhere, let not the care for it trouble you at all. This only I ask, that you will remember me at the Lord’s altar, wherever you be" (Confessions 9:27). And quotation upon quotation could be multiplied along these lines.
Prior to the Protestant Reformation, there weren't any Christians, anywhere, who did not have the custom of praying for the dead.
I remember hearing the story of an Anglican priest who had adamantly opposed prayers for the dead any time the issue was raised, and then after his wife's death he ceased to speak up on the matter, and was asked about it. He said that he had prayed for his wife every day, since he had met her, and could not bring himself to stop after her death. Prayer for the dead is a way the living show their love for dead. We also believe that prayers the dead are of some benefit to them, but exactly how these prayers benefit them is not something that the Church has precisely defined. If someone dies in a state of repentance, but without having had a chance to bring forth all the fruits of repentance, we believe that they are not ready to enter immediately into the presence of God, but that at some point, through the prayers of the Church, they will be. If someone dies in a state of impenitence, while our prayers are of some benefit to them, those prayers cannot make them worthy of the Kingdom of Heaven. But in either case, by praying for the dead, we strengthen our own faith, and come to better entrust our loved ones to God's mercy.