Campfires are allowed on the beaches, but the NPS asks that you make fires in elevated fire pans. Also, use a fire blanket to catch falling ashes and prevent them from scarring the beach. You must collect the ashes and take them with you -- campers are prohibited from simply dumping the ashes in the river.
Keep in mind that you're not allowed to collect firewood at all in the summer season. In the winter, you may only collect driftwood. During those winter trips, you should be on the lookout for piles of driftwood along the edges of the water. You can collect it throughout the day on your raft so you have enough wood for that evening. But even in the winter, it's best to bring your own charcoal or firewood in a dry container in case driftwood is scarce or you encounter some wet days.
Before handling or eating any food, be sure to wash your hands. The NPS says that hand-washing should ideally be done with treated water. Or, if you must wash your hands with river water, finish with some hand sanitizer. For the most efficient cleanup, it's best to do all your food preparation, cooking and eating over a tarp. When you're done, remove all the waste and shake the crumbs on the tarp into the river.