Short answers, pulled from the story.
The rex sacrorum, meaning "king of the sacred things," was a senatorial priesthood reserved for patricians in ancient Rome. According to the writer Festus, the rex sacrorum held the highest prestige in the ranking of Roman priests, above the flamines maiores and the pontifex maximus. Despite this rank, the office carried no political or military power.
After the kings of Rome were overthrown, certain sacral duties tied to kingship could not be transferred to elected magistrates. The rex sacrorum was established to fulfill at least some of those religious functions, while consuls assumed political power and military command. Whether the office was created at the founding of the Republic or had existed earlier in the Regal period is a matter of scholarly debate.
The rex sacrorum held a sacrifice on the Kalends of each month and announced the dates of festivals on the Nones. On the 24th of March and the 24th of May he performed sacrifices in the Comitium. He also appears to have served as the high priest of Janus.
The regina sacrorum was the wife of the rex sacrorum and a high priestess in her own right. On the Kalends of every month she presided at the sacrifice of a sow or female lamb to Juno. She wore a distinctive headdress called the arculum, made from pomegranate twigs tied with a white woolen thread.
The office was rarely sought because it conferred no political advantage, and some years passed with no rex sacrorum at all. By the time of Antony's civil war it had fallen entirely out of use. Augustus appears to have revived it, and mentions of the role survive from the imperial period, until it was probably abolished by Theodosius I.
The rex sacrorum was required to be born of parents who had married through the ritual of confarreatio, and he had to enter that same form of marriage himself. If his wife, the regina sacrorum, died, the rex was required to resign the priesthood.