2003 Ford Taurs

Could this be the timing belt/chain or water pump?
My 2003 Ford Taurus idles hard and the rpm's go up over 3500 when sitting at a stop light or when in park. The car accelerates when the gas is not touched and it's very hard to slow down because the idle is so hard. It sputters when I take my foot off the gas or when I do (very seldom now that it accelerates on its own!) Press the gas. When I shut the car off, the engine runs for about another 4 seconds before completely shutting off and makes a clicking sound when it finally does stop. About 2 weeks ago it was losing coolant so I bought "stop leak" and used it with no problems. Now, within the last 4 days it has started with this other problem.