I divided an Slc. "Tutakamen" a few days ago and this piece popped off.. Is it salvageable or am I wasting my time? Any advice on getting it to grow roots?
Can this Slc. division be saved?
Maybe. Are you asking how long until you have a blooming plant? How old are you? If the new lead grows roots it may bloom in three or five years. You can try setting it on sphagnum moss. Don't bury it or the plant will rot for sure. You can set it in a terracotta pot that has several inches of damp sphagnum at the bottom. Don't let the sphagnum dry out. You can put the pot in a tray that you add water to to keep the sphagnum barely moist.
It's growing roots! They look really thin, though. Should I wait until they get long and then repot, or repot now?
Very good. The roots should be about an inch long before potting the plant. Down at the very base of the plant you might notice one or more flattened green buds. They are referred to as the growing "eyes". Those will stay semi-dormant until the time when the plant has enough roots to support new lead growth and then they will begin to grow. Individual growing season also plays a part as to when these eyes will commence growth. Be careful not to handle that area of the plant and especially careful not to bury it when you pot or the eyes will rot. You will need a very small pot for a year or two. No more than three inches. Use terracotta. It breathes better while the plant is establishing. Also, use a fine bark mix because the new leads will probably be smaller than the parent plant since what's left has limited stored energy.
You will probably find the plant does not want to stay upright in its pot because of the short roots and long top. Growers use metal anchors on larger plants but you can secure your plant with a piece of thin coated wire like cable or telephone wire. Cut around eight inches of wire and make a loop in the center of the wire and around the straight lead. Cut two chopsticks down to about four inches and shove the pointy ends into opposite sides of the pot being careful not to hit those new roots. Wrap the ends of the wire around each chopstick. Voila! Your set.
Leave it alone. You can see new roots coming from the darkened area as well as above. You can also see the eye bud emerging. Disturb it as little as possible.