Short answers, pulled from the story.
The Constitution assigns three distinct functions to the office holder. They replace the president in the event of death, disability or resignation. They count the votes of electors for president and vice president before a joint session of Congress. They also preside over the Senate with the power to break ties.
The limited support structure began to change with the 1939 Reorganization Act. That legislation included an Office of the Vice President under the Executive Office of the President. John Nance Garner served as vice president at the time when this new administrative body was created.
Vice President Henry Wallace received actual executive duties during World War II. This shift granted him substantive powers beyond traditional legislative oversight. Alben Barkley later became a member of the National Security Council in 1949.
The Office of the Vice President has been located in the Eisenhower Executive Office Building since the 1950s. The space now includes emblems of the Navy Department coinciding with the office's original purpose. The vice president individually gained an office in the West Wing starting in 1977.
Jacob Reses currently serves as Chief of Staff to the Vice President. Bryan Gray holds the position of Deputy Chief of Staff to the Vice President. Ben Moss acts as Director of Domestic Policy to the Vice President.