The only way that you can remove the petcock or put it back on is to hold the petcock in its proper position, with respect to up and down, while you turn the nut. The nut is a special nut which has left hand threads on one end and right hand threads on the other. It has to screw onto the petcock at the same time it is screwing onto the tank fitting.
If you turn the entire petcock the brass tube attached to it will be bent all about and destroyed.
And yes, there is a fiber or plastic washer (either will work) between the petcock and the tank fitting.