What rope does the slingshot use? Is it an umbrella rope?

Generally, it is an umbrella rope, because it feels better, but what rope is wrapped around the handle of the slingshot has nothing to do with the elasticity of the slingshot itself. You can wrap a rag if you like. However, slingshots sold in the market are generally umbrella ropes, mostly made of nylon, because nylon is cheaper and durable, but nylon ropes do not absorb sweat and are uncomfortable to hold for a long time.