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Blooms fall off spontaneously. If you don't like the look of withered blooms, gently pull on them; they should release easily. If they don't, wait a couple more days. If you remove blooms too early, a small amount of clear sap will weep from the wound.

The usual and most reliable way to propagate Christmas cactus is by planting the individual green segments as follows:
https://www.gardeningknowhow.com/ornamental/cacti-succulents/christmas-cactus/how-to-propagate-and-plant-christmas-cactus.htm

However, you may be able to get the woody branch to grow by rooting it as described under Cactus Cuttings in the following article:
https://www.gardeningknowhow.com/ornamental/cacti-succulents/scgen/propagating-cacti-and-succulents.htm
Rooting hormones can help but aren't always necessary:
https://www.gardeningknowhow.com/garden-how-to/propagation/cuttings/root-stimulating-hormone.htm

I have several thoughts. 1. Christmas cactus is easy to grow from stem cuttings, even a single leaf; 2. You are likely to find very little soil and just a jumble of roots when you unpot it. Untangle the roots by briefly soaking the rootball. If you find roots supporting a stem, use pruning shears to make a clean cut then repot; 3. Christmas cactus can be pruned back to a more manageable size. Use pruning remains to start new plants. The less you handle/remove roots the better as the tiny feeder roots are easily damaged. https://www.wikihow.com/Care-for-a-Christmas-Cactus

It is considered non-toxic to dogs, cats and horses. ASPCA and PetMD have extensive lists of toxic plants.

First, I would not put the plant in the sun. It is already under a lot of stress and even when in good shape, it doesn't like full sun. Your leaves are likely to turn a reddish-purple color, at a minimum. They may fall off but this doesn't mean the plant is dead. After holiday flowering, there is a natural dormant period. Don't give up hope as I think you will start to see new leaves emerge in late February, if not sooner. Water gently - it doesn't need much while dormant. Fertilize when new growth starts but I would go easy and just use half the recommended amount until full recovery. If it was below freezing for over 24 hours, consider repotting the plant. This way you can look for dead roots and prune them out. They will be flaccid or mushy and a different color. If there are any intact leaves, consider taking a cutting to start a new plant in case this one doesn't pull through.
https://www.gardeningknowhow.com/ornamental/cacti-succulents/christmas-cactus/how-to-propagate-and-plant-christmas-cactus.htm

Hello

This would depend on the type of worms. If you can include a photo of them, then I can help you better. Usually, long thin white worms are ok. Red worms can be ok too, but some other types of worms can be harmful.

Here is an article on Christmas cactus care: https://www.gardeningknowhow.com/ornamental/cacti-succulents/christmas-cactus/advice-for-christmas-cactus-care.htm