For help with dividing these plants, this article will help: https://www.gardeningknowhow.com/ornamental/flowers/peony/dividing-peony-plants.htm
While these plants can be stored short-term, it is advisable to get them in the ground as soon as possible. That said, if you would like to try storing them, allow the rhizomes to dry out completely (up to five days). Place them in a ventilated bag with peat moss, and store this in a cool, dark area. Check weekly for signs of rotting. Peonies can be stored this way for a month or so until you are ready to plant them.