I leave the drying patches on the back steps and use them time and again for drying. The car-port allows them to dry from shooting session to shooting session.
The cleaning "patch" (the wet one used for flushing water into and out of the barrel) gets thrown out as there is only one- it is also used for cleaning out the hammer cup of the cap locks, and for wiping off the fouling from the bolster. The 4 drying patches are saved. The 5th drying patch is used for oiling the bore and other metal, like the lock's outer surface. So=- yes- you can use them over and over until they wear out.
No- they do not need washing as they are not dirty - only used for drying.