Short answers, pulled from the story.
Roman magistrates were elected officials vested with a degree of power called maior potestas. The most significant power was imperium, the authority to issue commands, held only by consuls and praetors. Any magistrate could veto the actions of an equal or lower-ranked magistrate.
The Roman Dictator held the highest degree of power, above even the consuls. Appointed only in military emergencies for a term of six months, the Dictator became the absolute master of the state. The last ordinary Dictator was appointed in 202 BC.
The Roman Republic was founded in 509 BC, at which point the powers held by the king were transferred to two consuls elected each year. The two consuls shared supreme civil and military authority, and their ranking alternated monthly between them.
The tribunician powers (potestas tribunicia) gave the emperor authority over Rome's civil government and made his person sacrosanct, so that harming or obstructing him was a capital offense. These powers were modeled on those of the plebeian tribunes under the old republic.
The traditional magistracies that survived were the consulship, praetorship, plebeian tribunate, aedileship, quaestorship, and military tribunate. Mark Antony abolished the dictator and Master of the Horse in 44 BC. The aedileship disappeared entirely during the 3rd century after losing its key powers.
Plebeian tribunes were elected only by the plebeians rather than by the full Roman people, which placed them outside the formal definition of a magistrate. Their authority rested instead on the sacrosanctity of their person; resisting a tribune was a capital offense, and they could physically interpose themselves to halt any action through a practice called intercessio.