I have read your blog on the bombing and I was thinking  about the innocent victims of Pearl Harbor who also died along with many others through the Japanese war machine and it owas merciless in doing so. 

Sure.  So was our slaughter of Indians at Wounded Knee.  That doesn't mean that slaughtering more innocents was the will of God.  A Japanese in your shoes would be just as wrong to speculate that Pearl Harbor was divine judgment for the slaughter of women and children at Wounded Knee as an American is to speculatet the Hiroshima and Nagasaki were somehow justified by the martyrdom of St. Paul Miki.

However, I concur that "Vengeance is mine" says the Lord.  On this day of remembrance, the homily alluded to some of these things that could have happened because of God's wrath.  For example, Japan had very little faith and many nonbelievers and Nagasaki was not even a target for the bombing, but it happened.  And, why were the Jesuits spared when the bomb fell on Hiroshima?  Did God have His hand in any of this? 

God has his hand in the fall of every sparrow.  That does not mean that God wills sin.  And the slaughter of innocents is grave sin.

As Christians, we strive to "be not overcome by evil but to overcome evil with good", and let God do the rest.  Did God have anything to do with the earthquake and tsunami in Japan in 2011--20000 plus died and some 300,000 were displaced and homeless?  Also, in 1995 some 6000 died in Kobe, Japan from an earthquake.  Is this a chastisement?

Chastisements are for us to discern about ourselves, not for us to claim to see in the lives of others.  Our part is to love victims and seek to comfort them.  Remember Job's friends, who were so sure they knew that Job got what he had coming.  The Lord rebuked them.

Do not some of the seers in Medjugorje discuss or talk about the chastisements for sins of this world? 

Medjugorje is a fraud.  Again and again the local bishops have warned that nothing supernatural is happening there, but the "visionaries" and their priest (who left the priesthood after getting somebody pregnant) have defied them.  So the bishops turned it over to Rome in the confidence that when they finish their investigation, Rome will repeat what the local ordinaries have been saying for years.

They even say that the Blessed Mother said there would be punishments for sins.  Is not this all the wrath of God?

That's what people said about Jesus as he hung on the cross.  Be careful of assuming you know who God is punishing.  They might be a saint or a martyr, like the worshippers at Urikami Cathedral incinerated by our bomb.  Or Christ crucified.  If you think it would be blasphemous to take a Host out of the tabernacle and set fire to it, consider how much more blasphemous it is to drop a nuclear bomb on it.  All we really know is that this was the wrath of man.  God has not told us it was his wrath and we should not presume to read his mind. Instead, we should avoid such speculations and obey him by not targeting and murdering civilians.

If we don't have confidence in God and know that we trust in Him, there will be no mercy when these chastisements are upon us. All of this is to take place in their life.

The way you show true confidence in God is to obey him.  He says "Judge not that you be not judged."  So don't try to pretend you know the mind of God about who is being punished, when they may really be suffering with Jesus on the cross.

What happens to those who don't believe and convert?  They say it will be too late. Is this the wrath of God and what happens when it's too late for them?  For even Jesus said that "the sheep would be separated from the goats"...

Those who truly reject Jesus and die impenitant will suffer the pains of hell.  But you do not know who these are.  So stop trying to figure out things too high for us and focus on doing what Jesus said to do: namely, caring for the least of these and loving your enemy, not speculating about their ultimate destiny.  Let him take care of sorting sheep from goat.  As people like Saul of Tarsus demonstrate, God has friend in very unexpected places and conversion happens to people we would never expect.