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Wilting is most often caused by having it temperatures under 50 degrees F. They need the same soil as orchids to do their best, so if you have transplanted it then it could be in the wrong soil type. If not, then it should still be in an orchid mix. They will need fertilization a few times per year with an orchid fertilizer as well.

You should keep the medium moist, but not wet or dry. They do not like to be dry, and they do not like to be saturated in water.

This article will help: https://www.gardeningknowhow.com/ornamental/cacti-succulents/christmas-cactus/advice-for-christmas-cactus-care.htm

Christmas cactus likes to be a bit snug so only go up one size container. Any container with drainage holes is fine. Alternately, plant into a plastic pot that fits inside a decorative container. Remove the plastic pot to water. https://www.gardeningknowhow.com/ornamental/cacti-succulents/christmas-cactus/advice-for-christmas-cactus-care.htm

The geranium looks OK to me but if you pinch off new leaves, it will force new leaves from lower down or at the base. The holiday cactus needs a new pot, one with drainage holes and more soil so it isn't sitting so low within the pot. When you repot, you may be able to separate a stem and root or one may break off which can thin be rooted in water for another plant. Prune back long stems to a lateral leaf or cut them out completely. The nature of this plant is to grow larger each year and fighting this, like trimming an overgrown bush, doesn't produce the best esthetics, in my opinion. This plant is easily rooted in water and then planted. In the long run, starting over with a cutting will have a better appearance than curtailing its natural habit. Houseplants don't need fertilizer over the winter and only monthly during the growing season. Over-fertilizing leads to lanky growth. Here is an article on pinching back geraniums. https://www.gardeningknowhow.com/ornamental/.../geranium/pruning-geraniums.htm

You're right, the article isn't clear. You should moisten the soil whether it's compacted or not. Christmas cacti tolerate drought well, but they do need water. We'll make some changes so the article is less ambiguous. Thanks for catching that!

Any kind of pot should be fine. It definitely needs a drainage hole - preferably several. Christmas cactus is one of those plants that likes water but can't stand to be wet for too long. You can read more about Christmas cactus care here: https://www.gardeningknowhow.com/ornamental/cacti-succulents/christmas-cactus/advice-for-christmas-cactus-care.htm
I've also changed the repotting article to try to make the steps more clear. I hope this helps. https://www.gardeningknowhow.com/ornamental/cacti-succulents/christmas-cactus/repotting-christmas-cactus.htm

No, you are not likely to get flowers the first year.
This article will help you with blooming.
https://www.gardeningknowhow.com/ornamental/cacti-succulents/christmas-cactus/how-to-make-a-christmas-cactus-bloom.htm