<<<<I want to know the detail biblical/ historical explanation of the ff:
1. Limbo >>>>

Well, limbo really doesn't have any Biblical basis. It was merely a theological opinion invented by St. Augustine to safeguard the absolutely necessity of Baptism. In John 3:5, Jesus very clearly says that without being born again "of water and the Spirit" (that is, without being Baptized), one cannot enter the Kingdom of Heaven. Now, this raised an issue: If someone cannot enter Heaven without being Baptized, what happens to babies who die before they are Baptized? On one hand, they have no personal sins. But, on the other hand, they are still under the curse of Original Sin. St. Augustine tried to solve this problem by proposing that unBaptized babies go to a place called "limbo" (which means "rim" or "edge" in Latin) --that is, they do not go to hell, but only to the "edge" of hell, which is not a place of punishment, but a place where souls are deprived from seeing God. This idea of Augustine was never fully accepted by the Church, but it was entertained as a pastoral measure so that Catholic parents would not neglect to Baptize their children. The modern Catholic perspective is that limbo is not necessary. What we believe is that Christ Himself can and does act when His Church neglects to act or when it is unable to act. So, if a baby is about to die without being Baptized, there is nothing to prevent Christ Himself from Baptizing this baby in some mysterious way. The Jesus Who we believe in would certainly do that because He is all-loving and all-merciful. So, limbo is, for the most part, a discarded theological idea. And a theological idea is all that it ever was. All that one must believe to be a Catholic is that some kind of Baptism (whether Sacramental through the Church, or mysterious and directly from Christ) is absolutely essential for salvation from hell.

<<<2. Paradise as used by our Lord for the good thief >>>


Yes. What Jesus said to the Good Thief was "This day you will be with me in Paradise." Now, Jesus could not possibly be referring to Heaven, since we know that Jesus did not go to Heaven "that day" --Friday. And, indeed, even three days later, when He rose on Sunday morning, He tells Mary Magdalene not to cling to Him because "I have not yet ascended to the Father" (John 20:17). So, Jesus and the Good Thief did not go to Heaven on Friday. Rather, as we are told in 1 Peter 3:19 & 4:6, Jesus spent Friday and all-day Saturday into Sunday morning in the realm of the dead (Sheol in Hebrew); and Sheol was divided into two places --1) Gehenna (a place of fiery punishment for sinners) and 2) a place called the "Paradise of the Fathers" or "the Bosom of Abraham," where the souls of the righteous awaited the coming of the Messiah so that they could go to Heaven. For, no one went to Heaven until Jesus ascended to the Father to "prepare a place" for us. And we see the "Paradise of the Fathers" or "the Bosom of Abraham" referred to by Jesus in Luke 16:22-24. This is the place where Jesus Himself went when He was dead for three days, and this is where the Good Thief joined him. In other words, the Good Thief's faith saved him from the punishment of Gehenna; and when Jesus said "This day you will be with me in Paradise," He meant that the Good Thief would be among the righteous Jews with Abraham and the other Old Testament saints who awaited the Messiah in "the Paradise of the Fathers."

<<<<3. The difference between Sheol and Gehenna of fire. >>>>

Well, again, .... Sheol (which means "the pit" in Hebrew) was the realm of the dead; and that realm was divided into two places --1) the "Paradise of the Fathers" or the "Bosom of Abraham" (which is where the souls of the righteous went to await the Messiah with Abraham, Isaac, and Jacob) and "Gehenna," which was a place of firey punishment. The name Gehenna actually comes from the Hinnom valley just south of Jerusalem, which was a place where the citizens of Jerusalem burned their garbage. So, it means a place of fire. Now, many Protestant assume that Gehenna is the same as hell. But, that's not how the Jews of Jesus' time understood it. They believed that one could be sent to Gehenna either for all eternity (i.e., hell) or only for a certain period of time, depending on how sinful you were. So, to the Jews, Gehenna could represent either hell or our concept of Purgatory. For example, when Jesus describes the rich man being sent to fiery Gehenna in Luke 16:22-31, we notice something interesting: After the rich man is told that there is nothing Abraham can do to help him personally, he then (in verse 27) begs Abraham to send Lazarus to his five brothers (who are still alive) to warn them to reform their lives so that they don't end up in Gehenna too. What this shows is that the rich man is still able to express selfless charity for someone else. He is still able to love other people. But, someone who is in hell is not able to do this. Those who are damned to hell love only themselves and couldn't care less if someone else is condemned. So, this alone shows us that the rich man is in Purgatory, not hell. For, as the Scripture says, "Where charity and love are found, there is God." And God is not in hell. Hell is separation from God and from His love. The rich man was not separated from love or the ability to love his brothers, and so not in hell.

God bless