Short answers, pulled from the story.
Maximian served as co-emperor alongside Diocletian, holding the title of Augustus from 286 to 305. When the Tetrarchy was formally established on the 1st of March 293 at Milan, he oversaw the western half of the empire and appointed Constantius as his Caesar. The system divided imperial responsibilities while presenting Rome as a single, indivisible inheritance.
Maximian had given Carausius command of his fleet, leaving himself without a navy when Carausius rebelled in 286. An invasion attempt in 289 or 290 was destroyed by storms. Britain remained under Carausius and then his successor Allectus until Constantius' forces retook it in 296.
Maximian hanged himself in July 310 at Marseille. He had been captured by Constantine after a failed attempt to seize the throne in Arles, and Constantine, while granting him some clemency, strongly encouraged his suicide.
Constantine initially declared a damnatio memoriae, erasing Maximian's name from inscriptions and purging his image from public works. After Constantine defeated Maxentius at the Battle of the Milvian Bridge on the 28th of October 312, Maximian's memory was rehabilitated. He was re-consecrated as a god probably in 317 and was appearing on Constantine's coinage as divus by 318.
Maximian's son Maxentius seized the title of Augustus on the 28th of October 306 and invited his father to return, saluting him as "Augustus for the second time." The succession following Diocletian's retirement had excluded both Maxentius and Constantine from the imperial college, leaving both men with grievances against the new arrangement.
Through his daughters Fausta and Theodora, Maximian was grandfather or great-grandfather to every reigning Roman emperor from 337 to 363. Fausta was the wife of Constantine; Theodora was the wife of the Caesar Constantius Chlorus.