According to history, Cato had long borne a grudge against Caesar for publicly embarrassing him. In brief, when they were both in the Senate, Cato spotted Caesar reading some correspondence while Cato was speaking, which was a pointed insult. Cato called on Caesar to read the letter aloud, which Caesar at first refused to do. Cato then invoked a public demand to hear the letter, whereupon Caesar read aloud an erotic love letter, which had been written by Cato's own half-sister, Servilia (one of Caesar's many lovers at the time). Cato never forgave Caesar for the insult.
Cato wears a black toga in contrast to other senators in order to stand apart from every other clique as a singular republican. This is historical fact, and indeed he had all rights to do it. Instead, when voting, he should wear a "toga dealbata", a completely white toga meaning that all senators are equal as their votes.
Caesar's need for the stolen eagles' return was not simple vanity. Like the samurai's sword, the eagle was regarded as the soul of the soldiers. By Ancient Roman law, if the eagle was lost, the entire legion was disgraced and should be broken up.
The opening battle scene is similar to the event Caesar describes in his Commetaries in which Pullo, after taunting Vorenus, attacks the Gauls single-handed and has to be rescued by Vorenus, then in turn Pullo attacks the Gauls who corner Vorenus. In Caesar's description, though, both men are centurions, friendly rivals but equals.
While having a chat riding looking for the stolen eagle, Vorenus says he's from Mutina (now Modena, in Emilia-Romagna Italian Region), Pullo says he's (probably) from Ubii tribe, a German one living near actual Cologne (Köln in German, now the biggest city of North Rhine-Westphalia).
In the first episode, Vorenus is referred to by Marc Antony as "2nd spear centurion". This means he would be the centurion in charge of the 2nd century of the 1st cohort of the legion. Later in the series, he is apparently promoted because his title is now "1st spear centurion", meaning he is now the "primus pilus" or senior centurion of the entire legion and advisor to Caesar or Caesar's deputy legate.