I just acquired a Christmas cactus. I don't have a window with indirect sunlight to put it in. However, I do have a table in the living room with a lamp that's on most of the day because my 91-year-old Dad sits in there watching TV for most of the day. Will the light from the lamp be sufficient for my cactus?
Probably not. If it is an incandescent bulb, then it will not provide near enough light, and too much heat. If it is an LED then it will need to be about 5 or 6 inches from the light bulb.
There are horticultural bulbs for plants that will fit into a normal socket, but still, you will need to hang these about half a foot from the light to a foot. A google search for horticultural LED will give you many results that will fit a standard socket.
Blooms on plant but not openning?
Can you put an image here so I can see what's going on? My guess would be low humidity. You can try spraying the plant once or twice per day. This can help.
Here is an article for more information on the care of these: https://www.gardeningknowhow.com/ornamental/cacti-succulents/christmas-cactus/advice-for-christmas-cactus-care.htm
I have a christmas cactus that is probably about 40 years old and is very large Should I divide it The root system is very thick
They tend to like being rootbound. It is not necessary to do so, but you can if you would like. https://www.gardeningknowhow.com/ornamental/cacti-succulents/christmas-cactus/repotting-christmas-cactus.htm
I got my Christmas cactus last year, and the blooms were the typical ones with folded back petals. This year, the buds just opened and lay flat. What causes this ?
Environmental stress can cause changes in flowers and the plant itself.
https://www.gardeningknowhow.com/ornamental/cacti-succulents/christmas-cactus/advice-for-christmas-cactus-care.htm
The brighter the light that your plant is exposed to, (but not direct light) will increase blooming and the actual blooms themselves.
Without seeing an image, it sounds like the plant is not receiving enough light to fully open the flowers.
i have other christmas cactus that are the same age , but are not dropping branches?
Most holiday cactus issues are due to moisture problems, too much direct sunlight or cold drafts. During winter when the plant isn't actively growing, it requires less water. On the other hand if the air in your home is very dry, the plant loses moisture at a higher rate. Using regular potting mix makes getting the moisture right more difficult. It stays too moist for too long and roots start to rot. It often helps to add coarse sand or extra perlite to the potting mix to speed drainage and drying. See if this article helps: https://www.gardeningknowhow.com/ornamental/cacti-succulents/christmas-cactus/limp-christmas-cactus.htm
My old plant has a section that is turning woody at the base and the leaves are yellowing and wilting. The plant was repotted last summer and another larger shout broke off at that time too. What can I do if anything to keep it alive.
The base of a Christmas Cactus turning woody is not generally a negative, but actually means the plant has been doing well and is just aging.
Yellowing leaves however can indicate a watering issue; either too much or too little. You should also check for pests or other signs of disease.
These links have more information for you.
https://www.gardeningknowhow.com/ornamental/cacti-succulents/christmas-cactus/woody-christmas-cactus.htm
https://www.gardeningknowhow.com/ornamental/cacti-succulents/christmas-cactus/yellow-christmas-cactus-leaves.htm
Buds start to appear but then just fall off, what is the issue?
This is a complex answer, with many reasons for this to occur. The most common issue is that it did not receive at least 14 hours of darkness per day prior to setting buds. There are many other reasons, though. This article will help you: https://www.gardeningknowhow.com/ornamental/cacti-succulents/christmas-cactus/christmas-cactus-bud-drop.htm