Short answers, pulled from the story.
Flavius Theodosius received imperial authority over eastern provinces on the 19th of January 379 at Sirmium. He ruled until his death in Mediolanum on the 17th of January 395.
The Theodosian dynasty made Nicene Christianity the state church through the Edict of Thessalonica issued on the 27th of February 380. They banned pagan worship by law on the 16th of June 391 and prohibited sacrifices intended to divine the future on the 21st of December 381.
Arcadius ruled the eastern provinces while Honorius took western territories following Theodosius's death on the 17th of January 395. Arcadius governed from Constantinople while Honorius operated from Milan and Ravenna.
Galla Placidia married Athaulf King of Visigoths in 414 and then wed patricius Constantius who became emperor as Constantius III in 417. Their children included Justa Grata Honoria and Valentinian III, creating complex succession claims that led to usurpations.
The House of Theodosius produced five emperors between 379 and 457 before their reign ended with extinction of direct male heirs. The Leonid dynasty succeeded them upon Leo the Great's accession.