Option 1: The statement that "its acceleration increases" is incorrect. When a body falls freely under gravity, its acceleration remains constant and equal to the acceleration due to gravity, which is approximately 9.8 m/s^2 on the surface of the Earth.

Option 2: The statement that "its kinetic energy increases while its potential energy decreases" is correct. As a body falls freely under gravity, it gains speed and its kinetic energy increases. At the same time, its potential energy decreases because it is moving closer to the ground or point of reference.

Option 3: The statement that "both its potential energy and kinetic energy remain constant" is incorrect. As discussed above, the kinetic energy of a freely falling body increases while its potential energy decreases.

Option 4: The statement that "its momentum remains constant" is not mentioned in the question. The momentum of a body falling under gravity does change, as it depends on both the mass and velocity of the object.

In conclusion, option 2 is the correct statement for a body falling freely under gravity, neglecting air resistance.