Short answers, pulled from the story.
The Reichstag building was constructed between 1884 and 1894. It was designed by Frankfurt architect Paul Wallot, who won an 1882 architectural contest that drew 200 participants. Wallot modeled the design on Philadelphia's Memorial Hall, the main building of the 1876 Centennial Exhibition.
The Reichstag fire occurred on the 27th of February 1933, four weeks after Adolf Hitler became Chancellor. Marinus van der Lubbe, a Dutch council communist, was identified as the apparent culprit. Hitler used the fire as a pretext to have President Paul von Hindenburg issue the Reichstag Fire Decree, suspending civil liberties and enabling a crackdown on political opponents.
Bulgarian-American artists Christo and his wife Jeanne-Claude wrapped the Reichstag in 1995. The project was financed entirely by the artists through the sale of preparatory drawings, collages, and early works from the 1950s and 1960s.
British architect Norman Foster redesigned the Reichstag for permanent use as a parliament building. The Bundestag convened there officially for the first time on the 19th of April 1999, the same day the keys were ceremonially handed to Bundestag president Wolfgang Thierse.
The glass dome on the Reichstag is a walk-in structure that provides a 360-degree view of Berlin and allows natural light to reach the parliament floor below. It was proposed by artist and architect Gottfried Böhm and was designed as a reference to the original 1894 cupola that had been dismantled during post-war restoration.
Under the 1971 Four Power Agreement on Berlin, Berlin was formally outside the bounds of either East or West Germany, which barred the West German Bundestag from assembling formally there. The building was used only for occasional events and exhibitions until after German reunification in 1990.