From your branch cuttings, you can certainly twist off some of the lower leaves, and they can also be rooted. Just put them by a warm, bright light area and wait patiently to make new roots or leaves.
Looking at your plant, it does need much more light, the color of the leaves is a give away, too deep green, typically the leaves are apple greenish in color if it is receiving good light and at times gets some reddish edging on the leaves.
My jades gets the reddish hues during winter, when it gets a combination of cold stress and lots of sunlight. And if it really gets very cold a lot of the leaves and branches turn red all over.
27Feb2012 - when we had some overnights in winter that went down to 20F for a few hours. Then some rains came at that time too in winter.