Water only when you feel it give a little if you very gently press it (I don't water on schedule). I have mine growing in pumice, too, so you can just imagine how dry that is. I've lost one before---a young one that literally burst from over-watering and that kind of mistake collapses the blob over a period of hours, not days. So when you feel it is turgid, leave it alone. I have mine in dappled shade most of the day and it gets only about an hour of direct sun in late summer afternoons. I also just got a pumice pot for it. I use these for succulents and cacti that scare me lol (like cintias, arios, some euphorbias and this one).

So you want a full grown plant to exchange with seedlings? That kind of makes no sense... I get that it rare, but still

That is just new 'arm' growing, and it will grow more of them White appendages are air roots, and are quite common on the plant that was originally used as a rootstock. It is most likely pitaya = dragon fruit = Hylocereus undatus. It will grow easily, just be aware it could get big. And very prickly !:) Rob - it is actually very common for rootstocks to continue growing, and well. They are much more vigorous plants than ones grafted onto them. That plant could potentially grow to 20feet - obviously under good conditions. That means lots of light, warm temps and best if it has something to climb on. It could be tied to some support, otherwise gets quite all over the place. It could die because of overwatering - same as most succulents. It is more common for grafted plant to die than rootstock.

You could just bury like a half inch with spines or I’ve heard of people, who have been doin this longer than I have, shave off an inch of the spines at the bottom. So it’s easier to place in the ground. Cut/slice off all the red. You’ll have to let it callus over for another week, but it’ll be sturdier in the mix. Roots will come out if you shave the lower part off or not. It’s just about if your worried if it’s gonna wobble out of it’s pot or not. The little ring pieces I would just set on top of soil/mix. No water or harsh sun till roots form. A spot protected from summer rains, but good strong filtered light. I’d say a month maybe a little longer you should have roots. Just leave it be. When roots come you can water and acclimate to stronger sun. I have a couple Mammillaria that are ground crawlers. You’re not the only one that has kept trying to prop up a crawler;). You can kinda tell which ones are gonna crawl even before they do. They have a look to them. Now that I see yours up close don’t think it’s a backebergiana, but still definitely a Mammillaria;). Some people plant them upside down to keep them from crawling on the ground. Pics from the Google.