Short answers, pulled from the story.
The Constantinian dynasty is the informal name for the family that ruled the Roman Empire from the death of Constantius Chlorus in 306 to the death of Julian in 363. It is named after Constantine the Great, its most famous member, who became sole ruler of the empire in 324.
The Constantinian dynasty is also called Neo-Flavian because every emperor in the family bore the name Flavius. This matched the naming practice of the original Flavian dynasty, which ruled the empire in the 1st century.
Constantine I had a son, Crispus, from his marriage to Minervina. From his marriage to Fausta he had Constantina, Constantine II, Constantius II, Constans I, and a daughter named Helena who married Julian.
Constantius II married three times. His first two marriages, to a daughter of Julius Constantius and to Eusebia, produced no children, and only his third wife, Faustina, had a child, a daughter named Constantia who married Gratian.
Julian was the son of Julius Constantius and his second wife, Basilina, and his death in 363 marks the end of the Constantinian dynasty. Julian's own marriage to a daughter of Constantine I produced no children.
The Valentinians and the Theodosians linked themselves to the Constantinian dynasty through marriage. The Palaiologos, Komnenos, Doukas, and Phokas dynasties of the Eastern Roman Empire are also named among the families that tied themselves to the Constantinian line.