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.

The “nipple” type cactus are so hard to id. Most the time when I see cactus like this my brain goes straight to Mammillaria, but I see more Coryphantha in yours. There’s also Escobaria. Hopefully it’ll bloom fairly soon for you. If blooms come from the top you’ve got a Coryphantha or Escobaria, but if the flowers come from older side growth it’s a Mammillaria. I’ve read the only way a person can tell the difference between Escobaria and Coryphantha is the seeds.

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.

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.