Some people will say there are three different cactus in this group and other will say 2. From the pictures you have shown, this variety will prefer to bloom either around Thanksgiving or Easter. The hint is the pointed edges on the stems. Christmas cactus have rounded edges. That does not mean it will not bloom around Christmas partly do to some recent genetic engineering and hybridizing of the different varieties.
Originally these plants were epiphytes which naturally grow on the limbs of larger trees in jungles of Brazil and similar environments.
They will prefer a bit more water, especially during blooms. You will know if you are over or under watering because the blooms will drop off before opening or limbs will break off. Because they are adapted to be on tree limbs high in the tropics, having their roots wet and then drain relatively dry is normal but the humidity is a bit higher than what most true cactus get. So you will need to experiment a bit to see where the watering in your particular home will match what the plants need. They are pretty hardy so minor mistakes probably will not permanently harm them. Once it gets a good growth on it, you can prune it and pot the cutting to experiment with in other parts of your home or give them to friends.
The plants naturally droop once the limbs get longer. I suggest looking at images of other similar cactus on line to see what the growth pattern can look like.
People do put them outside during spring thru fall. You just need to avoid any frost in early spring and late fall and toomuch direct sunlight. Growing in rainforests on tree limbs tend to limit the light they get.
They will acclimate to outside sun but may burn back a bit so gradually exposing them will help. I am in middle NY State so I will put them out on the north side of my house and slowly move them into more sunlight so they gradually get exposed to morning light. I do not keep them in full sun on the south side of my house. The sun gets too intense, especially in summer, and sometimes too dry in August.
The flowering is light sensitive so, if you have bright lights that you turn on during the Fall or Spring, this can disrupt the blooming cycle and they will not form flowers or the flowers will drop off. They need about 14 hr of dark for about 6 weeks to trigger the blooming. If you break this dark period with house lights, they may not bloom.
