Point B and point D are closer to the equilibrium position, and the resultant force is less than point C, so the acceleration of the object at point C must be greater than that at point D, so B is wrong.
C, in the process of moving from point C to point D (the direction has not changed), the gravitational potential energy of the object has increased by 1.0J, so the position of point C must be below the equilibrium position, so C is wrong.
D, the same kinetic energy corresponds to two positions in the vibration process, which is symmetrical with respect to the equilibrium position, so point D may be below or above the equilibrium position, so the acceleration direction of the object at point C and point D may be opposite, so D is correct.
So choose AD.