Yes u can camp
Turtleback Falls is right next to the top of Rainbow Falls- about a 5 minute walk from each other. I camped with 3 people and 2 dogs in one tent right next to Rainbow Falls. There's sufficient space for 2 camps because there were also 3 other people that happened to be there with us. We just shared a fire.
Yes, you can camp backpacking if you register...
No. But there are camping sites in Gorges State park which is where the trailhead for Rainbow/Tuttleback is located
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