While 'frame dragging' is the 'frame' just orbiting or is it even spiralling into the source of gravity? While 'frame dragging' is the 'frame' just orbiting or is it even spiralling into the source of gravity causing anti-dark-energy effect?
 A: During frame dragging the frame does spiral into the source of gravity and that how gravity works. The frame rotates because of the rotation of the gravitational body and the dragging is the cause of different bodies getting gravitationaly attracted to each other.
A: The frame dragging does not impart a sideways velocity. That is: if the infalling motion is straight towards the center of gravity to  begin with then the rotation of the source of the gravity will not manifest itself in the form of imparting sideways velocity.
What the frame dragging will do is that as the infalling object is traveling through the gravitational field it will rotate around its own center of mass.
(Of course, a rotation sensor (such as a gyroscope) that is co-moving with the object, hence local measurement, will not detect rotation. The motion through the gravitational field is inertial motion.)

Reference:
Andrew J. S. Hamilton and Jason P. Lisle, 2006 "The river model of black holes"
Journal reference:  Am.J.Phys.76:519-532,2008
