Inauguration Day is now always on January 20th. Before, it used to always be on March 4th. So, unless if January 20th is always a Tuesday, then, no, it is not always on a Tuesday.
Except for Washington's first inaugural, when he was sworn in on April 30, 1789, all presidents until 1937 were inaugurated in March in an effort to avoid bad weather. The 20th Amendment to the...
Yes. If January 20 falls on a Sunday however, the president elect is still sworn into office in a private ceremony, and then a public ceremony the following day.
Such celebrations are considered customary, but not invariable. In 1945, an increasingly ill Franklin D. Roosevelt, presiding over a war-wracked country, had no inaugural ball at all.