Short answers, pulled from the story.
The Theodosian dynasty ruled the Roman Empire from 379 to 457. It began when Theodosius I was made augustus at Sirmium on the 19th of January 379, and it ended with the death of the last emperor closely connected to the family in 457.
The dynasty's patriarch was Theodosius the Elder, a Hispanic general who saved Roman Britain from the Great Conspiracy in 368-369 and held the rank of magister equitum from 369 to 375. His son Theodosius I became the first emperor of the dynasty in 379.
The Edict of Thessalonica, issued on the 27th of February 380, made Nicene Christianity the official state church of the Roman Empire. It was one of several sweeping religious decrees Theodosius issued, which ultimately prohibited all pagan worship by 392.
The Theodosian dynasty produced five Roman emperors during Late Antiquity. They were Theodosius I, Arcadius, Honorius, Theodosius II, and Valentinian III, along with additional emperors who held the throne through marriage to dynastic women.
Galla Placidia, born in 392 or 393, was the daughter of Theodosius I and served as regent of the Western Roman Empire during the youth of her son Valentinian III. She kept western succession within the dynasty after her brother Honorius died without an heir in 423, and she died on the 25th of November 450.
The Theodosian dynasty formally ended in 457 with the death of the last emperor directly connected to the family. After Theodosius II died, power passed through marriage alliances: Marcian gained the East by marrying Pulcheria, and later emperors in the West held the throne through marriages to Theodosian women. Descendants remained in the East Roman nobility until at least the end of the 6th century.