Artifact Ghosting

Nick (gardenassistant) got it right for #1 & #2 haloes. They are caused when the haloed object is a distance in front of the object behind it that exceeds the depth of field. When the background object comes into focus, the foreground object is out of focus, and being out of focus, its boundary is blurred by the amount of the halo. The stacking software can't do anything about this since there is no image in the whole stack that has a focused part of the background object hidden by this foreground blur/halo.

HOWEVER, if you retake the whole stack at a higher f-number, you may well get the depth of field deep enough to bridge this gap between the foreground and background object, so get no halo. The higher f-number may not be exactly what you want as it might introduce diffraction blur, but this diffraction blur will be much much less than the original halo blur.

I would take both stacks at the same time, focus stack them separately to create two images, adjust them so they are exposure/colour matched, then combine them in Photoshop, either using a two-image focus stack approach or just masking out the haloed area to show the actual in-focus background from the second image.

What future versions of the Focus Stacking software should probably do is provide an option to fill these otherwise useless haloed areas with a content-aware / smart fill, or at the very least provide a mask to identify them easily so you can manually touchup later.