Short answers, pulled from the story.
Roman consuls held executive, military, and judicial authority over the Republic. They commanded armies of roughly 20,000 men, presided over the Senate and public assemblies, conducted elections, and served as Rome's chief diplomats. Within the city of Rome, each consul was attended by twelve lictors carrying fasces as symbols of his imperium.
The Roman consulship is traditionally dated to around 509 BC, following the expulsion of King Tarquin Superbus. The active consulship of the Roman Republic ended with the establishment of the Empire in 27 BC, and the office formally lapsed in the west in 534 and in the east in 541 under Justinian I. Emperor Leo the Wise abolished the title entirely in his Novel 94, issued during his reign from 886 to 912.
Lucius Sextius was the first plebeian consul, elected the year after the Licinio-Sextian rogations of 367 BC required that at least one of the two consuls each year be plebeian. Before that, the consulship had been restricted to patricians.
Each year was named after the two ordinary consuls who took office at its start, a practice known as consular dating. The year 59 BC was called the consulship of Caesar and Bibulus. Consuls took office on the 15th of March until 153 BC, when the date was moved to the 1st of January due to the Second Celtiberian War.
Under the Empire, consuls retained their title but lost most real power and became symbolic figures. Emperors nominated the consuls in practice, and frequently held the office themselves: Augustus was consul thirteen times, Domitian seventeen times, and Theodosius II eighteen times. The office became increasingly honorary and was eventually granted to teenagers and even children.
A consul ordinarius was elected at the start of the year and gave his name to that year in Roman consular dating, carrying greater prestige. A consul suffectus was elected to fill a vacancy created by the death or removal of an ordinary consul. Under the Empire, the suffect consulship was expanded by Augustus to create a larger pool of former consuls eligible for senior imperial appointments.