Who was the first Vice President to live in the Naval Observatory ? and when ?

The first full-time residents were Walter Mondale, President Jimmy Carter's vice president, and his wife, Joan, in 1977.

Gerald and Betty Ford were the first family eligible to live in the house. But the resignation of President Richard Nixon occurred before renovations on the house were completed, and the Fords headed to the White House. New Vice President Nelson Rockefeller, of the wealthy Rockefeller family, used the house mainly to entertain.

Where did the Vice Presidents live before the Naval Observatory was used ?

I think it was Blair House, but I'm not certain.

What is the Blair House used as now ?

Since 1974, Number One Observatory Circle, a house situated in the grounds of the observatory (formerly the residence of its superintendent), has been the official residence of the Vice President of the United States. - Wikipedia

Blair House is the official state guest house for the President of the United States. It is located at 1651-1653 Pennsylvania Avenue NW in Washington, D.C., opposite the West Wing of the White House, and adjacent to Lafayette Park. The main house was built in 1824 of buff colored limestone and is a late example of the Federal Style. The house was built as a private home for Joseph Lovell, first Surgeon General of the United States. In 1836 it was acquired by Francis Preston Blair, a newspaper publisher and influential advisor to President Andrew Jackson. It would remain in his family for the following century. In 1942 the house was purchased by the U.S. government and has since been the official residence for guests of the U.S. president. Blair House is primarily used to house foreign heads of state visiting the president, but it has also been used for domestic guests. Several presidents-elect of the United States have spent the night before their inauguration in the house, and President George W. Bush arranged for former First Lady Nancy Reagan to stay at the house and receive guests there following the state funeral for President Reagan.

Blair House is now a complex of four connected townhouses, including the original Blair House. During much of the presidency of Harry Truman, it served as the residence of the President of the United States, while the interior of the White House, which had been found to have serious structural faults, was completely gutted and rebuilt. On November 1, 1950 Puerto Rican nationalists Griselio Torresola and Oscar Collazo attempted to assassinate President Truman in Blair House.

During the 1980s, Blair House underwent significant restorations, with a new wing added to the north. An adjacent townhouse, Trowbridge House, is being renovated to serve as an official guest residence for former U.S. presidents while in the capital. The combined square footage of the four adjacent townhouses exceeds 70,000 feet, making it larger than the White House. - Wikipedia