Whole swathes of the bible were not included by the time of Constantine.
As to languages this sounds about right.
Aramaic is a Semitic language that was widely spoken from 600 to 200 B.C.E. in the near Middle East. It was one of the common languages of the region until the 13th century, when Arabic became more prominent. Many people believe Jesus and his apostles spoke Aramaic.
The Christian New Testament was written in the first century C.E. in the common Greek of the Mediterranean area and parts of the Middle East at the time. This form of Greek is called Koine Greek. It developed from classical Greek spread by the conquests of Alexander the Great. As different people began to use the tongue, it evolved and changed into Koine Greek between 300 B.C.E. and 300 C.E. This form may have been the second language of Jesus and his apostles -- after all, the gospels note that Jesus spoke with Pontius Pilate, who would have been more likely to understand Greek than Aramaic. The New Testament was probably written in Greek because it was the most common language around the Mediterranean at the time.
After the Roman Empire itself was Christianized and Latin become the common language, the entire Bible was translated into Latin. The first Latin version is called the Vulgate. In the mid-15th century, when Johannes Gutenberg invented movable type, the Latin Vulgate edition of the Christian Bible was the first work he printed.
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