Short answers, pulled from the story.
Hellenistic Greece began in 323 BC, when Alexander the Great died and his empire was divided among his generals. It effectively ended in 31 BC at the Battle of Actium, when Octavian defeated Cleopatra VII and Mark Antony, and the period fully closed the following year when Octavian took Alexandria.
Roman victories over the Achaean League at the Battle of Corinth in 146 BC destroyed the city and brought mainland Greece under Roman control. Full annexation followed later, ending when Augustus folded Greece into the Roman Empire as the province of Achaea in 27 BC.
The Diadochi were the former generals of Alexander the Great who fought a series of wars from 323 BC to 275 BC to divide his empire. Their conflicts ended the Argead and Antipatrid dynasties of Macedonia and brought the Antigonid dynasty to power.
Athens lost its independence after the Chremonidean War, which Ptolemy II encouraged the Greek cities to launch against Antigonus in 267 BC. The revolt failed, and Athens lost both its political independence and its democratic institutions.
Rome defeated Macedon's King Perseus at the Battle of Pydna in 168 BC and broke the kingdom into four smaller states. Macedon was annexed as a Roman province the year after a failed rebellion by Andriscus in 149 BC, and the Achaean League was crushed at Corinth in 146 BC.
The Achaean League and the Aetolian League were the strongest federations of the period, known as koinon, governed by councils of city representatives. The Achaean League controlled the Peloponnese except for Sparta, while the Aetolian League expanded into Phocis and defeated a Celtic invasion at Delphi.