As you may recall from the initial ray trace, a definitive, rotationally symmetric ring surrounded the hot spot of the detector.

"Ring" of Rays on Detector Viewer

It is possible that this ring of rays is due to multiple reflections off of the currently uncoated, FIRST CORRECTOR lens (Object 3).  To confirm this, we may again use the filter string capabilities. 

(Q3)  How are stray rays caused by multiple reflection in the first reflector affecting the total power at the camera?

The flag "Gn" refers to rays which are ghost reflected from parent segment's object n.  This flag only gets set for ray segments reflected from refractive objects when ray splitting is activated.  Let's observe the ray distribution at the camera from those rays (from both the star and the moon) which have ghost reflected from the first correcting lens. 

Filter For Reflected Rays

Filtered, Reflected Rays On Detector

The "ring" of rays are undoubtedly due to ghost reflections from the corrector lens, and accounts for a small, but measurable fraction (5.780E-006) of the total power on the detector plane.  To reduce the significance of these undesired rays on the camera, we may coat the corrector lens with an anti-reflective coating.