Do the Swarovski crystals have any of the qualities or energies of the gemstones of the same name, for example Peridot. If not, what special qualities do they have?
No, the only relation between man-made Swarovksi crystal and their natural gemstone counterparts are the color. Many of the crystal colors have been created to mimic or coordinate with the natural gemstone colors.
Natural crystals have served various purposes throughout the millennia, which has lead to the current belief that crystals stimulate healing. There are people who are convinced that there are healing properties that can be credited to using a specific combination of crystals and gemstones. You can find many books written about crystal properties. It's a fascinating study.
One special quality that Swarovski crystal does have is its spectacular beauty. They bring joy to many people through jewelry, statuary, stemware and home décor.