Thank you for the suggested ID. But I Googled for images and the photos came up quite differently! Could this one is something else? Some one... what do you think? Xuan

2nd photo: possibly Austrocylindropuntia subulata

Your Hens and chicks looks like Sempervivum 'Red Beauty'. Just in case you don't know, most Sempervivums need to be out in the cold in the winter so it doesn't make a great houseplant. A better garden plant for sure. i can't identify the so called zygo cactus from your picture. Maybe a closer shot? The third picture looks to be a sedum of some sort. These all look to be succulents, not cactus, to me. One last thing, most succulents are poisonous to cats so I don't recommend you let your cat eat any of them.

Irene General advice is not to use layer of pebbles on bottom of the pot. You did say:..."Putting pebbles in the bottom of a dish is the best thing so the water can drain out of the soil"...and if you meant saucer/drainage dish, then I am reading your message wrongly and misunderstood. Using layer of pebbles to raise the pot higher will work, but there is still standing water. If you mean container itself, there shouldn't be any layers. This is faulty advice that will temporary slow down possible rotting of the roots of plant kept without proper drainage - and that is potting mix, and the container. Container should have drainage holes - anything could be a container and look good, but drainage holes should be drilled in it. Different materials need to be thoroughly mixed, they should be of approx. same size to create fast draining mix, not layered. These are considered best growing conditions for succulents. Sure, you can grow in water retaining soil or in sand, or in a container without drainage and even in water - and plants may look fine for a while. But those are not best conditions for a long term of heath of plant, and even for convenience of the grower (has to be much more attentive to the watering...)