They eat what ever they catch raw if fire's a problem. As for the water problem, something that Mykel Hawke taught on a show called "I Shouldn't Be Alive, The Science of Survival:" When near questionable, or even stagnant water, go 12 inches out from the water's edge and dig down 12 inches or more into the sand or soil until water appears, it will be clean water.
Again, for literary credibility, one of your characters is going to have to have survival knowledge and skills, otherwise they'd most likely be dead. They can also use the tarp in conjunction with a fire the way Simon Kenton, the frontiersman friend of Daniel Boone did. When needing to warm himself with a fie while in the wilderness, yet keep it from the sharp eyes of the hostile Native Americans, he did the following. There is a fire lay called the "Dakota Fire Hole," and also one that's just built in a small hole/pit. If your characters were to build these at night or in the early morning fog that would come in off of the lakes in the early morning they would probably not be seen. Kenton would build a very small fire inside a pit about 8 to 12 inches deep, then sit in front of it, wrap a blanket around himself, up to his neck, with the edges of the blanket a bit past the hole so it wouldn't catch fire, keeping both smoke and flames inside the "wikiup-style" shelter. Simple, but highly effective. Fish and small game could also be roasted over the coals and water could be homogenized inside the plastic water bottles. The tarp could also double as a blanket as well as a camouflaged hide-a-way! Brown would be near invisible at night. Just some thoughts.
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