Short answers, pulled from the story.
The Byzantine senate was the continuation of the Roman Senate in the Eastern Roman Empire, established in the 4th century by Emperor Constantine I. It survived for centuries before finally disappearing in the mid-14th century under the Palaeologus dynasty.
Emperor Constantine I founded the Byzantine senate in the 4th century, establishing it in his new capital of Constantinople. His son Constantius II later elevated it from a municipal body to an imperial institution and expanded its membership to 2,000.
The Byzantine senate could pass resolutions called senatus consulta that the emperor might adopt as edicts. It functioned as a consultative body for imperial legislation, and some imperial pronouncements were read aloud before the assembled body. The senate also served as a court for high treason cases and held constitutional authority in the selection of emperors alongside the military.
Senators in the Byzantine senate were divided into three orders: the illustres at the top, the spectabiles in the middle, and the clarissimi at the bottom. During the reign of Justinian I, a fourth order called the gloriosi was created above the illustres to accommodate the highest-ranking senators.
The Byzantine senate's decline accelerated from the 7th century onward, as emperors Basil I and Leo VI stripped it of many formal powers through legal reforms. After the military faction's triumph under Alexios I Komnenos, the senate faded into irrelevance and the title of senator could simply be purchased from the emperor.
The Byzantine senate's last known act was to elect Nikolaos Kanabos as emperor in opposition to Isaac II and Alexius IV during the Fourth Crusade. The title of senator survived for a time under the Palaeologus dynasty before the institution finally vanished in the mid-14th century.