They are made to have a 40 hour spring power supply when wound completely. If you are having problems with your watch, take it to a certified Rolex watchmaker. Cheap Japanese and Chinese fakes...
No, all current Rolex models have "automatic" movements which means the watch is wound by hand and stays wound through the movement of your wrist. A half-moon shaped rotor inside the watch moves...
All automatic watches run a bit fast or slow. This includes Rolex. The only way to have a watch display the exact time is to by a quartz watch. Hope this helps.