Hi! So I’m trying to save the top half of a very small cactus. I’m not very optimistic because I had to cut off a large portion, and it’s not an easily-propagatable part (like a pad). The bottom half died because it had been planted in peat soil, and it never crossed my mind that the seller could have used the wrong kind of soil. I think the bottom has scabbed over, but I’m worried because some of the areoles are turning grey. The number of grey areoles has increased since I removed the cactus bottom (about two weeks ago) but the other half of the cactus looks perfectly green. The cactus overall and grey areoles are surprisingly firm, and I cut off a few of the grey spots and the inside still looks green (not rotted).
I have a couple questions about this:
1. Is this greying is normal/is it part of the healing process?
2. Will the cactus recover from this?
3. If it can recover, how long will it take for the cactus to put out roots? (How long should I wait before calling it quits?)
4. How should I care for it? Should I water it more frequently than a healthy cactus? Should I set it on top of soil?
Thanks in advance!

some of the areoles are turning grey

(bottom of the cactus)