There are 2 genus that make night blooming cereus. Hylocereus wich is called orchid cactus, and dragon fruit are often called night blooming cereus in the house plant and house hold identification. Hylocereus has many species that climb and make air roots for climbing and will climb trees or live in them and hang and bloom. They are non toxic with edible fruits if pollinated properly. I normaly just take a piece and put it in a well draining mix and not realy water it much. You can kill them if you over water them. The pieces will not die unless you kill them so they should grow in whatever you stick them in as long as you don't over water or over fertilize. If you live in a dry climate misting is a good thing. So basicaly just stick them in somthing and let them grow. Hanging baskets with coconut husks are good pots for them.

The other night blooming cereus is the true Cereus genus that are mostly column cactus and I grow them the same way. Just stick a cutting is some dirt and let it do its thing.
In my personal expierience in Florida sun the Hylocereus and true cereus do better in part shade with early sun.

I am not a proffesional these statements are just by my own expieriences.

it sounds like your talking about a Oxypetalum, if the leave are wide and flat, just put the cutting in a fast draining soil mix and mist 2 or 3 times a week, after it root you can water it lightly at first, they water when the soil is dry about 3 inches down, there fast growers and won't bloom until there about 3 yrs old,with any plant its better to be safe than sorry keep your plant up away from your cat, most cats will play with the leaves because they move and it becomes a toy, as far as making the cat sick I don't think it will, my crazy chihuahua plays with mine all the time and so far shes been fine

I live in SC and inherited one of these plants a few years ago. I almost threw it away last summer because it looked so bad. I found it listed in a 1950s houseplant book (had no idea what it was previously)- and realized it need a lot of sun (which I was not giving it). I put it in full beating down sun this year and it is the prettiest plant in my garden. I think I am going to transplant it to a huge hanging basket next year because I did a google image search and it is striking that way. Literally, it was a straggly nightmare last year, but in the sun w/ a little fish emulsion this year it is gorgeous, with about 15 bloom pods on it- one is blooming right now. What a nice surprise this plant turned out to be. FYI- I put it in a unheated poolhouse last winter and watered about once a month. It did get good indirect light from a window. I think I may throw a humidifier in this year.
Also, it roots sooo easily. When I hated it in spring and repotted it, a few pieces broke off. They grew right there on top of the soil for months. We are in a drought. No water, no soil, nothing. Crazy!