Statement I is correct: Satellite data (such as the GRACE mission) has confirmed that the Earth’s rotational axis is drifting and the speed of rotation is slightly changing. Since the late 20th century, this "Polar Drift" has accelerated and shifted direction.

Statement II is correct: Solar flares and Coronal Mass Ejections (CMEs) release high-energy particles and radiation that impact the Earth's thermosphere and magnetosphere. While this causes geomagnetic storms and affects satellite drag, it has no significant impact on the orientation of the Earth's rotational axis.

Statement III is correct: When massive polar ice sheets melt, the resulting water is redistributed. Due to centrifugal force, this water accumulates more near the equator than at the poles. This represents a major surface mass redistribution.

The Relationship: Statement III explains Statement I. In physics, when the mass of a rotating sphere is moved from the axis (the poles) toward the perimeter (the equator), the "Moment of Inertia" increases, causing a shift in the axis of rotation and a slight slowing of the rotation speed.