Bergzivman, at first glance I thought a Gymnocalycium, but the more I look the more I see a Lobivia;). Sorry not much help, but that's how cactus can be. Sometimes you just have to wait to see what the flowers look like. In this case you would only have to wait for buds to make a ruling if it's a Gymno or not. Gymnocalycium buds have zero spines, fuzz or anything. They're just smooth with a scale pattern;). Very distinct.

1)Opuntia something. 2) Cylindropuntia something Where do you live and are you growing these outdoors all year long? try posting on the Cactus & Succulent forum, not the C&S Gallery , but the actual forum.

The upright one in center looks like a Stapelia or at least one of the stapeloid group. Might also be some sort of Euphorbia. Can't see enough of the other to comment. Rapid draining soil and water only whet nearly or totally dry.

If I had to guess those marks are from frost damage and fungus. Almost looks like rust fungus, but I’m not a fungi master;). When you do take a cutting try to find the healthiest piece to root. If you want your Euphorbia cutting to look less scarred keep warm during the winter. California’s cold and wet winters can make for an unhappy Euphorbia.