You need those babies to start producing roots, so either pot them up, or put the whole clump in a pot, or suspend them in water, so that only the base is touching the water. This may, though, cause them to rot. They're easy to increase anyway just by digging up the clump, splitting it and replanting the sections.

Sedums don't seem to have much root at this time (or any time!!) of year. Pot them up, but cut the old dead stem off.

Thanks, they already have roots, but the plant is only about a centimetre big so far. Do i remove it from the dead stem and pot it? How often would i water it?

Yes, cut off the dead stem. Water immediately after potting on and then only when getting dry, if inside, probably unnecessary to water if outside.