Be careful not to overwater. Make sure they get plenty of light. In the first pic, the soil looks very dark. Is it wet? As for the last one, when you water it, take it out of the outer pot and let it completely drip off dry before putting it back (like an hour or more). Nice plants. Nice Mom!

Agj, Because they're actually missing the very bottom of the plant, its base, where the stem & rosette attach. Ill advised to root it w/ no stem whatsoever, as it would likely rot the very base of the plant & cause the whole thing to collapse. I wouldn't remove any bottom leaves at all, for fear of the same thing. I've never seen 'cuttings' of rosette type succulents w/ NO BASE or STEM at all. It's not something folks would normally do, if they'd grown these themselves as they'd know better, or anything that'd be done by folks who actually know these plants, that's why I'm suggesting return them if PURCHASED. Cuttings even if unrooted are comprised of the entire plant. Different if from a well-intended friend if they didn't know better. I once brought back a shopping back literally stuffed w/ cuttings from friends of a friend in San Diego. All the rosettes had some stems left on them at least an inch if not more. It's sort of the minimum that one needs. Imagine one quarter of a king size bed covered w/ newspaper & all sorts of succulent cuttings; almost all made it. For at least some of us, it doesn't have to be hit & miss at all. Since this person sounds like a Newbie, imagine if they plant these in soil & then watered? Major mush would likely follow. Kate: they are beautiful. From the IDs given, if you do some reading, you'll see they mostly require similar care; strong sun (except the Haworthia), moderate watering, small clay pots (must have holes in them) & fast draining mix. Good luck.

Thank you! I've just picked them up, so I haven't had much time to accommodate them, as I know they are growing a little big for their pot! I only live in the UK, so not much sun here, I'm afraid, but I do have a UV setup. Thanks for all the help! Edit: How do you know that the soil is the wrong type? Are there any indicators I should look out for? Thanks again!

It does look like Anacampseros...they can look so very different depending on growing conditions. Have a look at -this thread- and you'll see how different they look. Light, temps, watering - all will make difference.