1) The ball became live when tossed by the referee on the jump ball at the beginning of the game.
2) An airborne player retains the status they had when they last touched the floor. Therefore, a player who jumped from their frontcourt and deflected the ball back while airborne did not return the ball to the backcourt, even if they landed there.
3) The ball does not become dead when touched by a player after the shot clock signal sounds, unless the ball is in its upward flight on a shot for a field goal.