The Julio-Claudians, Rome's first (and probably most famous) dynasty, started in 27 BCE with Augustus and ended in 68 CE with the assassination of Nero. The Julio-Claudians set the tone for the first few eras of Roman rule; good emperors tried to behave like Augustus, bad ones tended to err on the side of Caligula or Nero. In this way, the Julio-Claudians function as a lesson in the power, capability and debauchery of the emperors of Rome. 

Legend has it that Livia, Augustus' second wife, ran almost as much of the empire as he did. When the time came for a successor to be chosen, Tiberius, Livia's son, was the only logical choice, being the only male with the experience to conceivably manage the empire. In this way, the Claudians became the most powerful family in Rome, reigning until the assassination of Nero decades later. 

Actually, none of the Julio-Claudians were preceded by their natural-born father. Adoption, especially among noble families, was common in the Roman world. Especially because the position of emperor was so important, emperors normally strove to pick the best heir possible, although this was not always the case. As for the Julio-Claudians, Tiberius was Livia's son, but not Augustus'; Caligula was her great-grandson and Claudius her grandson. Nero was Claudius' great-uncle. 

Julius Caesar, Pompey the Great and Marcus Crassus attempted to "split" the power of the Roman Republic between the three of them, with Caesar taking Gaul and Crassus heading east. Eventually, the death of Crassus, as well the untimely demise of Pompey's wife (who was Caesar's daughter) led to the end of the triumvirate and civil war between Caesar and the Senate (led by Pompey). Augustus Caesar, Marc Antony and Lepidus would later form the second triumvirate, which would also end in Civil War.

The correct answer is "none of the other answers" because the Roman Empire's system of government did include a Senate, two popular assemblies (comitia centuriata and tributa), magistrates, and censors. 

The correct answer is "none of these". The popular assemblies in the Roman Empire lacked all legislative powers. 

The Flavian dynasty, which rose with Vespasian out of the Year of the Four Emperors, and was the first dynasty after the Julio-Claudians. It consisted of Vespasian and his sons, Titus and Domitian. It ended with the assassination of Domitian, which predictably led to civil war. 

The tetrarchy was formed by the Emperor Diocletian in 293 CE after a series of disastrous civil wars in the Roman Empire. Diocletian divided the empire into four districts, each administered by a central imperial authority. This division lasted for about two decades, until the establishment of an Eastern Roman Empire led by Constantine and a Western Roman Empire led by Licinius.

The Five Good Emperors ruled the Roman Empire from 96 C.E. until 180 CE and presided over the greatest period of territorial growth, peace, and prosperity in the history of the Roman Empire. In order of their reign they were - Nerva, Trajan, Hadrian, Antoninus Pius, and Marcus Aurelius. Caligula, on the other hand, who reigned for a few years in the first century CE, is known to popular history as a tyrant and a madman.

The Han Dynasty was a contemporary of the Roman Empire and reigned from approximately 210 BCE until 220 CE Economic depression and uneven land distribution contributed to the decline of the empire as civil conflicts and peasant rebellions broke out, periodically weakening the authority of the centralized government; epidemics of virulent diseases led to widespread chaos and disorder; and conflict between the ruling elites further fractured the political infrastructure. The decline of the Han Dynasty, which had been weakening for several decades, was completed in the early third century with the conquests Dong Zhuo.