Short answers, pulled from the story.
Diocletian was Roman emperor from 284 until his voluntary abdication on the 1st of May 305. Born Diocles to a family of low status in the Roman province of Dalmatia, probably between 242 and 245, he rose through the military ranks to become the longest-serving emperor of the late third century.
The Tetrarchy, meaning "rulership by four", was the system Diocletian established in 293 when he appointed Galerius and Constantius as junior colleagues (Caesars) alongside himself and his co-Augustus Maximian. Each of the four rulers governed a quarter of the empire with his own court, army, and administration, and they were linked by marriage and formal adoption.
Diocletian launched what became known as the Diocletianic Persecution beginning on the 23rd of February 303, after court officials interpreted an oracle's response as blaming Christians for obstructing divine prophecy. His co-emperor Galerius pushed strongly for persecution. Diocletian himself had earlier been conservative in religion, applying similar reasoning to Manicheans before targeting Christians.
The Peace of Nisibis, concluded in 299 after Galerius's victories over Narseh, required Persia to return Armenia to Roman dominance, designated Nisibis as the sole trading point between Rome and Persia, and granted Rome control over five satrapies between the Tigris and Armenia, including Ingilene, Sophanene, Arzanene, Corduene, and Zabdicene.
Yes. On the 1st of May 305, Diocletian became the first Roman emperor to voluntarily abdicate his title. He assembled his generals and troops at the same hill outside Nicomedia where he had been proclaimed emperor and removed the imperial vestments in a public ceremony.
Diocletian's Palace, built near the small town of Spalatum on the Dalmatian coast, is preserved in large part today and forms the historic core of the modern city of Split in Croatia. UNESCO designated it a World Heritage Site in 1979.