When ever I put my car in park and release the brake pedal, my car rolls forward, then the shift knob moves also, Its an automatic so I dont understand why this happens,
Is it normal, or should I have it checked out?
It sounds normal to me. When you stop the car with the brakes, it usually won't have all the teeth of the gears (and all other moving parts) resting perfectly against one another - this is called the backlash in the system. With your foot on the brake its going to stay in one spot, but once you release your foot, the car can easily roll forward (a few inches) until there is no more slack in the moving components.
Its the same explanation as why you can move the steering wheel on your car slightly without changing the tracking. At least on older cars and those that don't have drive by wire steering systems.
It is deffinetely normal for it to roll a little. Just like stangdude said, there can be a little backlash in the gears, but also the transmission holds the car in place with a parking pawl, which is basically a toothed wheel and a pin or block that engages the wheel to hold the driveshaft in place. When you stop and put the car in park, it may have to roll an inch or two before the pawl engages one of the teeth on the wheel.
The shifter moving could be the same thing, if you mean it just sorta twitches a little. The shift lonkage is directly connected to the parking pawl, so when you put it in park it is all in a certain position, but then once the car rolls and the pawl engages, the linkage will move slightlt due to the pawl "snapping in", so the shifter, of course, will move slightly.
So if it is no more than a few inches that the car rolls, and the shifter just jerks slightly, I would not worry at all.
EDIT: Also like Art said, even with an automatic trans it is reccomended that you use the parking brake rather than relying on only the pawl. You can actually brake a parking pawl by rocking the car hard enough. The owners manual probably says to put the parking brake on before you let go of the brake, this puts the force required to hold the car on the parking brake, rather than on the pawl.