Short answers, pulled from the story.
The Roman King of Rome held absolute authority as chief priest, lawgiver, judge, and sole commander of the army. He organized troops, selected leaders, conducted campaigns without restriction, and controlled all state property including land and war spoils.
The Roman Republic emerged in 509 BC when power shifted from the executive king to consuls. Two consuls were elected annually with supreme civil and military authority that flipped ranking monthly throughout the year.
Roman dictators were appointed for six-month terms during military emergencies when constitutional government dissolved temporarily. They became absolute masters of the state until their specific crisis resolved before resigning once matters concluded successfully.
Emperors held imperium existing through legal standing rather than election alone combined with tribunician and proconsular powers. These powers gave them control over civil government, command over the Roman army, and authority reserved previously for senate and assemblies including declaring war and ratifying treaties.
Traditional magistracies remained available only to senatorial class members initially within the cursus honorum career path. Non-senatorial citizens could run if permitted by emperor or appointed directly instead of following standard republican procedures.