Short answers, pulled from the story.
Koine Greek was the common supra-regional form of Greek spoken and written during the Hellenistic period, the Roman Empire, and the early Byzantine Empire. It served as the lingua franca of much of the Mediterranean and the Middle East, and it is the language of the Christian New Testament and the Septuagint, the 3rd-century BC Greek translation of the Hebrew Bible.
Koine Greek arose as a common dialect within the armies of Alexander the Great. It spread from the Ptolemaic Kingdom of Egypt to the Seleucid Empire of Mesopotamia and replaced the existing ancient Greek dialects with an everyday form anyone could understand. The post-Classical period of Greek is defined as beginning with Alexander's death in 323 BC.
Koine Greek differs from Classical Attic Greek in grammar, word formation, vocabulary, and phonology. Key phonological changes include the loss of vowel length distinction from the 2nd century BC, the replacement of pitch accent with stress accent, and the collapse of several diphthongs into single vowels. The consonants beta, gamma, and delta also shifted from stop sounds to fricatives.
Yes. The Roman Emperor Marcus Aurelius wrote his private thoughts in Koine Greek in a work now known as Meditations. The text was a personal notebook, not intended for public readership.
Koine Greek continues to be used as the liturgical language of the Greek Orthodox Church and in some Greek Catholic churches. It also developed further into Medieval Greek and ultimately informed Modern Greek.
The most significant sources are post-Classical inscriptions and papyri, valued for their authenticity. Other sources include the Septuagint, the Greek New Testament, Greco-Latin glossaries from the Roman period, and Modern Greek dialects, which have preserved some oral features that written texts lost.