I don't grow these chlorophyll-free plants, some say that they are short-lived but I don't know if that applies to all of them or if it is the combination of this Gymnocalycium species with the Hylocereus stock that has a limited lifespan. I once degrafted a dark purple one, and it looked happy, but I would not try that with a completely red plant. So, the "broken off balls" (offsets) should be grafted, not rooted. I hope they are still attached to the mother plant, they need to be in good condition for the graft to succeed. Anyway, if I would make my own grafts of a "ruby ball" on a tough stock I would try Opuntia humifusa (or the variant O. compressa). That one is probably the hardiest of all cacti, and it does not seem to induce as much offsetting as some other grafting stocks. Echinopsis/Trichocereus species are often used too, they are relatively hardy. Three less hardy alternatives are Selenicereus, Harrisia and Myrtillocactus geometrizans. I have only tried various Opuntia, Selenicereus grandiflorus, Pereskiopsis spathulata and a Hylocereus (the two latter is not useful in this case). There are many good places that describes the process: http://www.cactus-art.biz/technics/Grafting_on_opuntia_compressa_index.htm http://www.cactiguide.com/forum/viewtopic.php?t=6799 http://www.youtube.com/watch?v=IPy_01OSDUg http://www.youtube.com/watch?v=Bda1k09CqaM (in Dutch, but it shows the technique) This one can be of interest to you ... http://www.youtube.com/watch?v=3nQYJ7PmQEQ Be prepared for a few failures, it takes a while before you get everything right. Now is not the best time of the year to do this, the plants need to be growing. Late spring/summer is better.

Cutting away the softened parts is not enough, all of the discolored tissue must be removed. If the soil is the thing sold as cactus soil ("SÃ¥- och kaktusjord") in Sweden it means peat with some lime and sand. Even if a cactus can survive in it for years it is risky to use, as it retains too much water, becomes too compact with time and fungi thrive in it. Cuttings do not need to lie in the sun, I always keep them in a shaded spot until they have rooted. It can take a long time in winter, and if it is a big cutting I let it heal until February before rooting it, instead of trying to force it. Actually the whole plant does not need much light now, the 60 W bulb will do more bad than good, as the heat encourages the plant to grow at the wrong time of the year. The thin shoot is extremely etioliated and should normally be cut off and discarded, but it should be possible to root it as an emergency rescue. The other offset looks better but still not good. An ordinary incandescent or fluorescent lamp will not provide enough light, it needs to be placed in a sunny window, or outside (during the growing season, that is). It should not be watered from early autumn to mid-spring.

The second one is an Echeveria runyonii also known as 'Topsy Turvy.' I would not pot them together as they are all very different plants. It will be easier to monitor and nurture them if they're in individual pots. They each need a well-draining mix in a well-draining pot. The cactus and succulent mix you have will work well if you cut it with Perlite. A good place to begin is 50% Perlite to 50% soil mix. You can find Perlite at any nursery or Big Box store like Home Depot. It's relatively inexpensive. You can try beheading the stretched one. Let the cutting callous for a couple of days, then stick in the potting mix. Do not water it until you see growth. Keep the stem along with the pup. I'm not sure about this, so perhaps someone with more experience can chime in. When you do repot, add potting mix up to the top rim of the pot. That way your plants can get maximum air circulation. Good luck!

That looks like Aloe juvenna, very easy plant to grow. Cuttings grow easily; I posted some photos on this thread I can't think of the reason for leaves to be wet? Did she pour water over? or it got rained on? If plants keep rotting, it must be watering issue. Soil plant is in looks like peat, not really suitable to grow succulents. Cuttings, just potted: