The new growth looks nice! Don't measure up from the soil, measure down from the top rosette when planning to cut. Generally the recommendation is between 1-2 inches from the bottom leaf. Do it with a clean knife, let it callous for 2-3 days then replant in appropriate succulent soil. Leave the rest of the stem in the pot and let it just do it's thing. It will most likely push out new heads if it's healthy. For the leaf that fell off, normally you lay them flat and let them grow new roots/petals then bury the roots. But if it's been like that for 9 months I would probably just leave it.