Gigi,
Plant #1 looks like he came through well and is now going through its bloom cycle. I'd consider letting it bloom which probably means not pruning until early spring. It would be cool if some roots appear from the foot on the rock as you could train them over. Since the foot is in the air you might notch (tiny V) the circumference where you would like to see a root form and dab some root stimulator on the notch.
Since it had rot I would water it and #2 with some Cosan 20 fungicide (or equivalent) as a preventative measure soon and then again when it starts to get cold.
Plant #2 is adorable and it's trying to make it. You can see the tips barely poking out, but it looks like it had a harder time with your procedure.
A caudex stump can produce new roots if all of the rot was extracted. Planting air roots in "soil" may be dangerous, but I'm not sure because I've never done it with adeniums. (Help on this from someone).
If it has no roots it's important to provide it an easy medium to grow new roots into. I believe that James recommended sand which is less prone to foster rot and easy on new roots.
No roots makes it hard to provide stability. I would tie it down gently but firmly so that the plant feels secure.
I'm a big fan of rooting powder and fungicide when treating rot.
Bright indirect light or early morning light would be best for weeks and keep it moist but not wet (like a cutting).
#2 reminds me of one of my Arabicum seedlings with a beautiful darker pink flower that developed root rot. I had to cut 70% of the caudex off. The plant tried to callous but the loss of tissue was so large that it sucked into itself forming a convex bottom. I worried about leaving an air pocket so I planted it in an inorganic mixture of sand and fine coco peat. The poor little thing has made 2 attempts to leaf out only to fail from lack of roots. After 1 year of babying this plant I think that it's going to make it!
It's rooted enough to support a small amount of leaves, but the recovery has been painfully slow.
Here is a picture of a same aged sibling for comparison.
) to follow those videos of undoing the knot or stretching the roots and putting rocks (or styro) in between the adenium roots so they can breath and encourage developing big caudex. (You know those videos that show you how to do it and make it look really easy.) 
) so as you can see, my adenium has totally no roots. I put cinnamon on the cut and it is sitting on a sanitized bottom of a styro cup. It has a dry fresh media.
Did it early this morning and just pulled it out of the pot and letting it enjoy the morning sun. Then will most likely just air dry in the garage for a week just to be sure. Cut looks healthy so far!
based on his observation of middle plumeria cuttings ) "It is trying to do two things at once so it has a harder time of recovery." I should have could have left the stems intact, just remove some leaves. But i didn't know any better and now more sprouts or tips are coming up and I am confident it is going to make it. The air root is an experiment worth taking since I felt like I had nothing to lose. I think the bottom caudex is developing roots as well, which could later on be trained. 
