Back many years ago, when I was in the bou scouts, we would use a pine cone as a scrubber to scrub put the cooked on food. We would generally use a little bit of drinking water or extra water left to put the fire out with.

As far as where to wash, I have read some posts or information from various backpacking sites that said to walk about 50 feet or 50 yards, can’t remember which, and wash your dishes there so bears and other wild animals won’t pick up on the scent at your camp site.