Q.Succulents and rot
My question is simple. If some of the stems are detaching themselves from the main part of the plant, would that be considered rot? What should I do for this? I noticed some black spots and cut them off of the plant already.

If the stems are detaching, it may not be rot. Are the stems firm or soft? Softness would indicate rot. It may be that they are responding to growing conditions (less light than they would prefer?) I agree with the above answer in that pictures would be helpful. And sulfur is a good treatment for rot. I used it successfully on a very old, large Christmas cactus which had stem rot. I removed all the soft, rotted tissue, getting down to firm, healthy tissue and then applied sulfur powder directly to the wound.

The best thing is always preventative. Wettable sulfur can help cure it if it can be cured. Pictures would help here if you can put them. You can also try putting peroxed at 1 part peroxide to 3 parts water. This can help as well.
The best thing would be to let it dry out thoroughly between waterings. These will not tolerate wett soil for very long.