Short answers, pulled from the story.
A Roman dictator was an extraordinary magistrate of the Roman Republic granted full state authority to resolve one specific problem. The power to appoint a dictator normally rested with the consuls, one of whom could nominate a candidate without consulting his colleague; after nomination, the dictator's imperium was ratified before the comitia curiata.
Roman dictators were required by customary law to give up their powers immediately after completing their assigned task, and most are recorded to have resigned as quickly as possible. The common claim that a dictator was limited to six months is contradicted by recorded practice; Livy records a dictator explicitly objecting to a six-month limitation as unorthodox.
The formal reasons, called causae, included military emergencies (rei gerundae causa), holding elections when consuls could not (comitiorum habendorum causa), performing a religious nail-driving rite to protect against pestilence (clavi figendi causa), quelling sedition, holding the Roman games, and in one exceptional case after the Battle of Cannae, appointing senators.
After the Second Punic War of 218-201 BC, Rome's major wars moved to distant theaters and lasted for years, making the short-term dictatorship unsuitable. The rise of promagistrates gave Rome more long-term commanders in the field, and the Senate began using the senatus consultum ultimum rather than a dictatorship to handle domestic crises.
In 82 BC, Sulla had the dictatorship revived through legislation passed by the comitia centuriata, appointing him to write laws and reconstitute the state, with immunity for all past and future actions. Traditional dictators were bound by centuries of custom to act for all Romans and resign immediately on task completion; Sulla used the office to impose wide-ranging reforms before resigning on the 1st of January 79 BC.
Mark Antony, Caesar's former magister equitum, abolished the dictatorship after Caesar's assassination in 44 BC. He passed legislation making it unlawful to propose, vote for, or accept any dictatorship, with summary execution as the penalty for anyone who became dictator.