Below link should help you https://www.recreation.gov/camping/campgrounds/251575
Yes there are some small camping areas by the lake
I don't know but I see two more knowledgeable guides already answered.
There are some camping areas. The link provided above will help you find one.
I was there only for one day, I spent most of the time by the waterfall, I didn't see it , so sorry I can't help you with your question
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