Short answers, pulled from the story.
Augustus was the first Roman emperor of the Julio-Claudian dynasty. He was born Gaius Octavius and was adopted by his great-uncle Julius Caesar, taking the name Gaius Julius Caesar upon adoption.
Tiberius died on the 16th of March AD 37 at the port town of Misenum at the age of 78. According to Suetonius, the Prefect of the Praetorian Guard, Naevius Sutorius Macro, smothered Tiberius with a pillow to hasten Caligula's accession.
Caligula was murdered on the 24th of January AD 41 by the Praetorian tribune Cassius Chaerea and his men. His wife Caesonia and their infant daughter Julia Drusilla were also killed on the same day.
Claudius was eventually poisoned, possibly by Agrippina, in AD 54. He had adopted Nero on the 25th of February AD 50, making Nero heir to the throne over Claudius's own son Britannicus.
The Julio-Claudian dynasty ended with the suicide of Nero in AD 68. Nero became emperor in AD 54 at the age of sixteen and was the fifth and last emperor of the dynasty.
Yes, the bloodline of Augustus endured into the era of the Nerva-Antonine dynasty through descendants of his first granddaughter Julia the Younger. Tiberius's lineage may have survived into the 2nd century through the offspring of his granddaughter Julia Livia.