Looks like Senecio mandraliscae, Blue Chalk Sticks. Yes it will root from cuttings and possibly from leaves (altho I have never done that). New plants will sprout from the stems, as you seem to have starting.

Mine likes to sprawl along the ground, so don't be surprised if it wants to lay down.

Awesome, thanks Crenda.I would assume a normal cactus mix soil to repot this?

You can use the cactus mix if you cut it in half with some perlite. You want it to drain well.

I'm a proponent of the gritty mix because my plants are outside and it is waaay too rainy in the summer for almost any other mix. But adding the perlite has worked, too.

Good luck! I am sure it will perk up for you.