The curve used is exactly the same as that which is used for the Spline Component (which is the same curve that Matinee uses too). It performs a cubic interpolation against (currently) auto-calculated tangents. The curve passes through its control points. Tangents are auto-calculated to be of uniform length and with no ‘breaks’.
Rotations are also interpolated in a similar fashion - this also performs a cubic interpolation, this time using Squad quaternion interpolation. If control points contain no rotation, then no rotation will be applied to bones controlled by the spline IK node.