I would take apart that branch and start a new pot. The main plant probably needs to be repotted. Clean out as much as the old potting mix you can, trim the roots a bit and put it in a new fast draining mix. You can search 5-1-1 mix here and repotting. There are lots of explanations. If you are on Facebook there is a group called Holiday Cactus Lovers group with lots of helpful people. Most of them prefer to repot using a fifty fifty mix of potting soil and perlite. If you repot, tale your time and read up here. I'm happy to answer specific questions if you need it. My weekend will be busy so it might take a bit before I respond. If the clades on the fallen branch are withered, sometimes they can be saved by putting them i a ziplock baggie full of water for a day or two. Just flip the bag every day. I actually forgot about one for about two weeks and it had sprouted roots. Good luck!

I tend to disagree with some of the advice in that link: sand for play boxes is usually too fine, it is specifically good packing sand to make sand castles and sand cookies and similar...if it was coarse, it would not stick together. So that info is, IMO, incorrect. You need to find what is referred to as Horticultural sand - much grittier, with bigger particles. Most of us do not use sand at all (very few ppl do, and they have lots of knowledge and experience with growing succulents). You would be much better off reading info on this forum: ppl giving advice grow (and many, like Jeff above), have been growing succulents for years. Our goal is to keep plants healthy, and #1 is usually drainage problem: mix needs to drain fast/well, and soil with fine sand will not provide drainage. Perlite is available to most. It is good idea to sift or rinse it, to get rid of dust. Pumice is anorher excellent substrate, not always readily available. Chicken grit/small granite gravel, is another ingredient excellent to use. There are many more inorganc ingredients that could be used. MG bagged potting soil is considered not good enough and many will not use it (including me). You could make much better draining mix by using just sifted perlite and Cactus&Succulent soil in 1:1 ratio. If you already have MG soil and want to use it, I would suggest to add even more perlite (60-80%). If you have pumice, use it instead of perlite. Or mix it with perlite, and use much less soil. Adding grit helps a lot. Grains of different ingredients should be approx. of same size: 4-6mm is good. It could be tad smaller, but, IMO, 2mm or less is too fine. Over 6mm gets to be too large. Many succulets do not need very large pots. Try to find out where some grow naturally: most in very 'rocky' areas, with literally no soil (or very little), and many on and in-between the rocks: tight spaces. So size of the pot is not always a problem. Bigger is not neccessarily better :) Repoting is usually not needed every year, and if repotting, it is better to go up just a bit - if plant needs it. Succulents could be grown in large pots - but drainage is even more important. Lots of water retaining soil that will fill up large pot will take very long time to dry up and cause lots of damage. If you provide good drainage (and have space for it), you can grow tiny plant in a wine barrel.... There is ton of info here, from good and experienced growers. Not like on some blogs, that offer incorrect info (at least partially) - often not based on experience, but incorrect info passed down. ETA: I just re-read blog you posted link to: here is contradicting info offered within 2 or 3 paragraphs: ..."The type of sand I buy is just the stuff they sell for use in a sandbox (I buy it at either Home Depot or Lowes)"... ..."Just don’t use sand from the garden, the beach, or a sandbox (you never know what nasties will be in that sand)"... Do not use play sand - either from the bag or a sandbox... Anything will work for short period of time. But if you want to grow succulents for a long time, keep them healthy - try to provide good drainage and good light.

Thanks! I look forward to hearing more too, neighbor gave me that last summer and it's been a lot of fun, has bloomed a lot, more blooming than growing. If it wasn't for the great advice I got here, it would probably be dead by now. I thought the 'cactus' part of the name meant it wanted to be really dry most of the time, and luckily was told right away, that's exactly wrong, and to give it airy, chunky soil without sand in it. I keep snapping off pieces to share with other people, and have stuck about half a dozen pieces in the soil of the same pot. None are big/tall enough to peer over the rim yet though some have some tiny new leaves down in there. I'd still call it slow-growing but it's hard to say since I've shrunk it on purpose so often. Always open to tips for improvement!

This cactus definitely likes more water than other cactus, but still let them go dry before watering again because they can rot. These guys hang off the cliffs of Bolivia in the jungle. So their roots are constantly being washed with water, but their roots are never ever sitting in a wet mix. A good gritty mix would work nicely. I keep mine hanging in a mini apple tree, but obviously you can't do that in your zone. They like bright filtered light. Not direct sun. Definitely do not like the cold. So far Monkey Tail has been one of the easiest and fastest growing cactus I have grown:).