Short answers, pulled from the story.
The vice president has three constitutional functions: replacing the president in the event of death, disability, or resignation; counting electoral votes before a joint session of Congress and declaring the winners; and presiding over the Senate with the power to break ties.
The Office of the Vice President was formally created under the 1939 Reorganization Act, which placed it under the Executive Office of the President. John Nance Garner was the sitting vice president at the time.
The Office of the Vice President is primarily housed in the Eisenhower Executive Office Building, where the vice president's ceremonial office is located. Additional offices exist in the West Wing (provided since 1977), the United States Capitol, and at the vice president's official residence.
Because the vice president's formal duties are tied to the Senate, staff salaries are funded through both legislative and executive branch appropriations. This dual-branch funding arrangement reflects the vice president's unique constitutional role straddling both branches.
Roger Sherman, a Connecticut congressional cabinet member and Founding Father, argued that if the vice president did not serve as president of the Senate, another member would have to fill that neutral role, making the Senate disproportionate. His argument helped establish the vice president's presiding role in the chamber.
The vice president was first given an office in the West Wing in 1977. Prior to that, the office was centered in the Eisenhower Executive Office Building, where it has been located since the 1950s.