Short answers, pulled from the story.
Octavian was born Gaius Octavius in 63 BC, the great-nephew of Julius Caesar. After Caesar's assassination on the 15th of March 44 BC, he accepted Caesar's will, which made him heir to three-quarters of the estate and gave him the right to use Caesar's name. Historians call him Octavian during the years 44 to 27 BC to distinguish him from the dead dictator.
The Second Triumvirate was created by the lex Titia, passed on the 27th of November 43 BC, establishing Octavian, Mark Antony, and Marcus Aemilius Lepidus as co-rulers with consular power, the right to appoint magistrates, and authority over Rome's western provinces. Unlike the informal arrangement between Caesar, Pompey, and Crassus, it was a formal legal office ratified for five years.
The proscriptions were a systematic outlawing and killing of political enemies begun by the triumvirs in late 43 BC. Roughly 300 senators and equestrians were declared outlaws and killed, with thousands more losing their property. Each triumvir sacrificed someone in his own circle: Octavian permitted the killing of Cicero, Antony proscribed his maternal uncle Lucius Julius Caesar, and Lepidus proscribed his brother Paullus.
The Battle of Actium was fought on the 2nd of September 31 BC in the bay of Actium along the Ambracian Gulf of western Greece. Octavian's fleet, commanded by Marcus Vipsanius Agrippa, defeated the combined naval forces of Mark Antony and Cleopatra. Cleopatra's ships withdrew early in the fighting, Antony followed, and his remaining land forces surrendered to Octavian.
In 32 BC, Octavian seized Antony's secret will from the temple of the Vestal Virgins and published its contents publicly. The will planned to distribute Roman-conquered territories as kingdoms to Antony's children by Cleopatra and requested burial next to Cleopatra in Alexandria. Octavian used the will to persuade the Senate and Roman public that Antony had abandoned Roman values in favor of a foreign queen.
Cleopatra took her own life by poisoning after the fall of Alexandria on the 1st of August 30 BC, having met with Octavian and refused to be paraded in a Roman triumph. The ancient sources do not support the popular belief that she died from an asp bite. Octavian ensured she was buried next to Mark Antony in their tomb.