Short answers, pulled from the story.
The Supreme Court of the United States first convened on the 1st of February 1790 inside the Merchants' Exchange Building in New York City. The court heard no substantive cases until 1791 despite holding its inaugural session from February 2 through the 10th of February 1790.
John Jay served as the first chief justice after President George Washington nominated him to lead the Supreme Court of the United States. Six justices including John Rutledge, William Cushing, Robert H. Harrison, James Wilson, and John Blair Jr received Senate confirmation on the 26th of September 1789.
Marbury v. Madison asserted judicial review allowing the Supreme Court of the United States to invalidate acts of Congress that violated the Constitution. Chief Justice John Marshall made this power central to the court's identity during his tenure from 1801 to 1835.
The Supreme Court of the United States opened its permanent building designed by Cass Gilbert in 1935 after occupying various spaces within the Capitol for over a century. The four-story marble structure sits at One First Street NE near the Capitol and contains a courtroom plus justices chambers.
The Supreme Court of the United States receives approximately 7,000 petitions for writs of certiorari annually but grants fewer than 80 cases. The rule of four allows any four justices to grant review while most denials occur without comment leaving lower court rulings intact.