2003 Saturn Ion care accelerates

While standing at red lights, I notice that my car is accelerated as if I HAVE MY FOOT ON THE PEDAL. When I look at the RPM dial, it reads slightly over 1. Sometimes I place the car in park, press on the pedal, and the car accelerates up to 2 or 2 1/2 and it takes a while for it to get back down to 1, then all is quiet and well. However, by the time I reach the next stop, the car is again accelerated. I feel like I have to press down hard on the brakes or my car will take off. Also, when I slow down, by pressing on the brakes, the car kicks 2 times before I come to complete stop. I'm guessing this has something to do with the acceleration as well? Anyhow, can anyone tell me what heck is going on with my car and what needs fixing?
Thanks!