The original language of the Old Testament was Hebrew followed by Aramaic translations appearing in the period following the Exile and then Greek translations following Alexander the Great. It was not until around the 2nd Century, A.D. that the contents of the Old Testament had become fixed.
The original language of the New Testament was Greek. As with the OT, no originals now exist, and the oldest of the manuscript copies dates from the 2nd Century, A.D. Before the NT was "canonized" into its current form, each of the early Christian communities apparently had a gospel of its own, in some ways redundant, in some ways in direct conflict, with the gospels of other communities. Some of these included the Gnostic Gospel of Thomas, the Gospel of Hebrews, the Gospel of the Ebionites, a Gospel of the Egyptians, an Apocalypse of Peter, an Apocalypse of Paul, and the Epistle of Barnabas, to name just a few.
What the Christians used as an "infallible" Bible was different depending on which Christian community you talked to, at least until the year A.D. 325. In that year, Emperor Constantine convened the Council of Nicea, which not only did the picking and choosing of the books, but also ended a power struggle in Christian circles as to the nature of Jesus. As Roman Emperor, Constantine decreed that the Trinitarian view would become Christian dogma (which is remarkable considering how weak his Christian credentials were), and this decree silenced the large Christian segment that said Jesus was only a man.
Of course, the history doesn't end there. As the Bible was translated into Latin, Augustine ultimately complained of the "infinite variety" of Bible translations. Under the direction of Pope Damascus, Jerome attempted to standardize the Latin Bible. Drawing on Hebrew, Greek, and Latin, he completed the "Vulgate" by sometime around A.D. 405, which was ultimately recognized as the Standard Bible of the Roman Church (1546).
The first English Bible was completed in the late 1300's by John Wyclif, an Oxford instructor in religion and philosophy. Condemned by the church, it lasted in the underground for some 150 years. Then, around 1524, William Tyndale, an Oxford and Cambridge educated linguist, who was influenced by Erasmus and Martin Luther, published a New Testament translation based on medieval Greek copies. Then Mike Coverdale's Bible appeared (~1535) based on his translation of German and Greek translations, as well as drawing from Tyndale's work. John Rogers and Richard Taverner also published their particular translations (~1539) drawing from and adding to each other and to Tyndale's work. All of this was eventually edited by Coverdale into the Great Bible, which the King approved. Separately, the Roman Catholic church created its first English Bible, the Douay version, which was based directly on the Latin Vulgate (~1609).
In 1604, King James I wanted a fresh start, and pulled together Oxford and Cambridge scholars, as well as Puritan and Episcopal priests. This large group used the Catholic Douay, Luther's German translation, the available Hebrew and Greek copies, and to a very large extent Tyndale's work, and created the King James Version (~1611). Language, of course, is a fluid thing. Just how fluid can be seen in just a few examples: In 1611 "allege" meant "prove," "prevent" meant "precede," and "reprove" meant "decide." To cope with this, the English Revised Version came out by 1885, followed shortly by the American Standard Version.
It is important to understand in which sense your opponent believes the Bible to be infallible. In the first sense, contradictions and factual / scientific errors are all one needs to falsify the claim of Biblical infallibility. In the second sense, the notion of infallibility is simply irrelevant to both the Bible and the oldest sources we have available today, and so amounts to little more than an empty claim.