Short answers, pulled from the story.
Octavian sailed to Italy and landed at Lupiae near Brundisium shortly after the Ides of March in 44 BC. He received a copy of Caesar's will there, which made him heir to three-quarters of the estate.
Octavian accepted the inheritance by appearing before the urban praetor on the 8th of May 44 BC. This legal act allowed him to assume the name Gaius Julius Caesar Octavianus as Caesar's adopted son.
Only 2,000 legionaries were sent by Octavian to Antony while traveling with his wife Octavia. These troops proved insufficient to replenish Antony's lost forces against the Parthian campaign.
The Battle of Actium occurred on the 2nd of September 31 BC along the Ambracian Gulf of western Greece. Octavian's fleet led by Agrippa defeated Antony's forces, leading to their eventual defeat at Alexandria.
In 27 BC, Octavian reached a formal settlement with the Senate for control over half of Rome's provinces and most of its armies. This agreement marked his transition from Octavian to the first Roman emperor known as Augustus.