Overwatering is the likely culprit. Let the plant dry out a bit more between waterings. It could also be caused by too much direct sunlight. Keep it in a spot that gets bright but indirect light.

Unfortunately, Christmas cacti are not very tolerant of cold temperatures and extreme temperature changes, so yours may have a hard time recovering. The best you can do now is to keep it in a warm place with bright, indirect light and care for it normally. Make sure it is kept moist but not wet—overwatering can cause wilting, too. 

While you wait for the plant to recover, perhaps you should try to start a new plant from one of its branches? 

Bud drop is a common problem with Christmas cacti. Sudden changes in temperature, lighting, and watering can cause it to occur, so even the act of bringing it home from the store and into a new environment could have set it off. Now that the plant has adjusted to its new home, it shouldn’t drop its buds, as long as its care is kept consistent.

It sound like too little water and/or too much direct sunshine. Is it planted in cactus soil (a special mix); you could try that as it better controls the moisture than traditional potting soil. And remember, though it is a cactus, it comes from the humid forests of Brazil, where it lives epiphytically on tree branches, meaning that it doesn’t sit in water, but doesn’t get bone-dry either.

Water it a little and gradually a little more. Do not soak it. And allow it to dry out between waterings. Too much moisture in the soil will cause the plant to rot (leaves will drop). Water sparingly but consistently in fall and winter, and keep it out of direct sunlight, just give it bright, indirect sunlight.

In theory this could work; the only thing that might be an issue is water. Christmas cacti like warm, humid, shady environments, but will not tolerate being over- or underwatered. So if you do plant them outside, make sure you place them in an area where the soil doesn’t completely dry out nor stay wet for too long. Good luck!

If the sections have roots already, they can be replanted. If not, their stem ends should be placed in slightly moistened soil, sunk about an inch or so into the soil. After about six weeks, they should have roots and can be transplanted to larger pots.

Christmas cacti don’t need to be pot bound to grow, though they do prefer it. Your cacti’s lack of growth probably boils down to an issue with either light or water, however. 

Christmas cacti like bright, indirect light, so an eastern window is ideal. Keep them out of direct, intense sunlight, as this can burn their leaves.

As for water, these cacti are a tropical species, so they require more water than the usual cacti. That said, they don’t like to sit in water, so use a well-draining potting mix (such as a succulent mix) and a pot with drainage holes. Water when the top inch or so of soil is dry.

Your best course of action would be to repot both cacti in a well-draining potting mix in separate pots with drainage holes, then see if they do any better than they are now!