Short answers, pulled from the story.
The Hellenistic period began with the death of Alexander the Great on the 10th of June, 323 BC, and most scholars place its end at 31 or 30 BC, the years of the Battle of Actium and the Roman conquest of Ptolemaic Egypt with the death of Cleopatra VII.
The nineteenth-century German historian Johann Gustav Droysen coined the term in his work Geschichte des Hellenismus to describe the period when Greek culture spread into non-Greek territories after Alexander's conquests. It derives from the Ancient Greek Hellas, the name for Greece.
The three dominant successor states were the Ptolemaic Kingdom in Egypt, the Seleucid Empire across the Near East, and Macedon under the Antigonid dynasty. Smaller kingdoms including Pergamon, Pontus, Bithynia, and Cappadocia also held significant territory.
Koine Greek, a common dialect based on Attic Greek, became the lingua franca of the ancient world during the Hellenistic period. It was used in administration, trade, and religion across territories stretching from Greece to central Asia, and later served as the language of the New Testament.
The Hellenistic period produced the mathematical works of Euclid and the scientific writings of Archimedes. The philosophical schools of Stoicism, Epicureanism, and Pyrrhonism all developed during this era, and the Library of Alexandria became the ancient world's foremost center of scholarship.
Hellenistic culture reached as far as modern Afghanistan, Pakistan, and northwestern India. The Greco-Bactrian kingdom held territory covering most of present-day Afghanistan, and Indo-Greek kings ruled parts of northwestern India until around AD 10. Strabo records that Greco-Bactrians had contacts with Han China through Silk Road trade routes.