Does it needed to replace head screw and screws when replace head studs???
 

Does it really needed to replace head screw nuts and screw washers when replace head studs??? If yes, why???

No you can reuse the barrel nuts and thick washers. Just make sure the tooling/hex in the barrel nuts are not damaged and the threads are good. Otherwise future removal can be difficult.

The washers are very thick and strong. I would check the surface of the washers where the nuts have beared down on the washer. If they are marred from tightening of the nuts, or dented from loose nuts, you can file the surface smooth.