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I would steer clear of drafty locations, but the use of a plant light should be ok in addition to placement in a sunny window. These plants should also be kept moist. Should be ok to divide plants. This article will help as well: https://www.gardeningknowhow.com/houseplants/aralia-plants/polyscias-fruticosa-ming-aralia.htm

Spring is the best time to transplant. This article will help you with avoiding transplant shock:
https://www.gardeningknowhow.com/plant-problems/environmental/learn-how-to-avoid-and-repair-transplant-shock-in-plants.htm

It's most likely due do the fact that you're trying to root them in water. If you wish to propagate this plant, place the cuttings in some damp SOIL. Keep the soil damp and the cutting should root in just a few weeks. For additional rooting success, place the pot and cuttings in a plastic bag.

http://houseplants.about.com/od/foliageplants/p/MingAralia.htm
here is a link to ming care. it doesnt sound like that is the type of plant u have, they are not bamboo.but for any plant its best if you remove and throw out the old soil. u can rinse the roots with hot water. u can also treat the soil with epsom salts or rubbing alcohol,dish soap and water mix

Plant them in nice light soil or potting mix! Rooting plants in water is pretty much a myth. Roots that grow in water are different than roots that grow in soil. So when you put the rooted cuttings into soil, they still have to grow new roots!
Put them into soil in small pots, or pot, keep them in bright indirect light, and when you're ready to travel, roll up some paper towels and pack them tightly over the top of the soil, then wrap some heavy brown paper firmly around the pots and up past the top of the foliage, and carry them in a bag that you can keep protected and upright.

This article should help you with its care: https://www.gardeningknowhow.com/houseplants/aralia-plants/polyscias-fruticosa-ming-aralia.htm