Short answers, pulled from the story.
Illyricum became a formal Roman province in 27 BC as part of the constitutional settlement by which the Roman senate formalised Augustus's rule. It was initially a senatorial province but became an imperial province under Augustus in 11 BC.
The province covered what are now Albania, Bosnia and Herzegovina, Croatia, Hungary, Kosovo, Montenegro, Serbia, and Slovenia. It combined Upper Illyricum, also called Dalmatia, with Lower Illyricum, also called Pannonia, and was administered from the capital Salona near modern Split, Croatia.
The Batonian War was a four-year rebellion from 6 to 9 AD led by two commanders who both bore the name Bato: Bato the Daesitiate and Bato the Breucian. It was triggered when Dalmatian and Pannonian tribes recruited as Roman auxiliaries turned against Rome instead, and it required Tiberius and Germanicus to quell it with multiple legions.
Several emperors were born in the Illyrian region. Claudius II, Quintillus, Aurelian, and Probus were all born in Sirmium, modern Sremska Mitrovica in Serbia, and are called the Pannonian emperors. Diocletian was born in Salona, Constantine the Great in Naissus, and Justinian I in Tauresium near modern Skopje.
The province was divided into Dalmatia and Pannonia during the reign of Vespasian, who reigned from 69 to 79 AD. Epigraphic evidence, including a military diploma dated to July 61 AD, suggests Pannonia existed as a separate entity at least since the reign of Nero.
The First Illyrian War of 229-228 BC broke out because the Ardiaei tribe, based in what is now Montenegro and northern Albania, had raided Roman allied ships in the Adriatic Sea and invaded Greek cities including Epidamnos and Pharos. Rome intervened with a powerful fleet, freed the Greek cities, and forced peace terms on the Ardiaei.