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If the plant is dormant, or nearly so, you can transplant the rhizomes now. Cut off the remaining foliage and remove dead, shriveled rhizomes.

It can be just a little confused, if the temperatures are a little cooler. Maybe this is the case? Otherwise, it is just a fluke this year. Typically these will bloom in spring. Here is an article for more information on the plant: https://www.gardeningknowhow.com/ornamental/cacti-succulents/christmas-cactus/advice-for-christmas-cactus-care.htm

Bleeding hearts are perennial and grow easily from seed. They perform best with morning sun or filtered shade and moist soil. In mid-summer heat, the stems/leaves begin to look ragged. At this point, you may prune them back or cut them to the ground and they will remain dormant. They bloom in spring and are not repeat bloomers.

Actually it is best to not deadhead your Bleeding Heart.
Just let it die back naturally.

There are several Dicentra cultivars and native varieties. They share the need for afternoon shade with morning sun and rich, moist soils. They are intolerant of dry and wet soils. Dicentra spectabilis, from Asia, is the largest and most likely to go dormant mid summer in hot, dry weather. If this happens, the foliage gets yellow and ratty-looking, so cut it down to the ground. Dicentra eximia is native to Eastern US, is smaller but blooms mid summer. "luxuriant" is a hybrid with nice foliage that doesn't usually go dormant but does not bloom mid-summer. The main bloom is springtime but it may rebloom in the fall. If your soil is average fertility, dig 3-4 inches of compost into the top 6 inches. Fertilizer isn't needed but add 1 inch of compost annually. As to hanging planters, popular choices are petunias, fuchsia, wild yam, silver licorice plant, some begonias, trailing or climbing zonal geranium, Black-eyed Susan vine, nasturtium and Callibrachoa.

They should start to flower relatively early. This may mean that it is lacking fertilizer, or the pH is off. I would add dolomitic lime to buffer the pH, and fertilize once per year, at least, with an all-purpose. This article will guide you on the care of these: https://www.gardeningknowhow.com/ornamental/flowers/bleeding-heart/bleeding-heart-care.htm