Short answers, pulled from the story.
Gaius Vibius Pansa Caetronianus was the first of the Vibii to hold the consulship, serving in 43 BC. He led Roman forces at the Battle of Forum Gallorum against supporters of Marcus Antonius and was mortally wounded in the fighting, dying shortly afterward.
Vibius is an Oscan praenomen, a personal given name that became the family's nomen. The Vibia gens itself was probably Oscan in origin, and the name appears frequently in Campania but was also used in Latium and at Rome from an early period.
The emperors Trebonianus Gallus and his son Volusianus each claimed descent from the Vibia gens. Both were proclaimed emperor in AD 251, following the death of Hostilian, and both were slain in August of 253 as the general Aemilian marched on Rome.
Vibia Sabina was the daughter of the consul Lucius Vibius Sabinus and became the wife of the emperor Hadrian, serving as Roman empress from AD 117 until her death around 136. Her father had married Salonia Matidia, the niece of Trajan, linking Sabina to two successive imperial dynasties.
The two Republican cognomina were Pansa and Varus, both of which appeared on coins. Pansa translates as splay-footed, and Varus means knock-kneed; each originally described a physical characteristic of the person to whom it was first applied.
Vibia Perpetua was said to have been a young mother who was martyred as a Christian at Carthage in AD 203. Her name links her to the Vibia gens, though the sources do not specify her relationship to other known members of the family.