Mechanically unnecessary, perhaps, but very necessary from a symbolic point of view, making sure that the President (bearing in mind that the first President had just replaced a King as Head of State) is emphatically placed as the servant of the people rather than as a potential tyrant.
Maybe, but the wording in this case is quite unambiguous as to when the President's term begins (and it's not when the oath of office is administered). A rarity for the US Constitution, I know, but it does happen.