is the cactus in good condition?

Question

they have kind of black or gray at the base of the cactus but top look good…and how to save it and propagate it?

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Answer 1

No, it doesn't look good. It may be rotting from the roots up. You can try repotting in fresh cacti soil but it's probably a good idea to propagate. You can cut off a couple of those stems above the dark color. Make sure you only get healthy tissue. Let it callous over for a few days before placing in new container with fresh cacti potting mix.

https://ucanr.edu/sites/mgslo/newsletters/Propagating_and_Caring_for_Cactus28082.htm

https://www.gardeningknowhow.com/ornamental/cacti-succulents/scgen/overwatering-cactus.htm