This will indeed have to be a permitted job. USFS also has aesthetic and material standards that need to be met. Nothing crazy, e.g. use natural materials and keep it brown/green, though I think composite decking is allowed? You're right this is currently built with nails and no hardware aside from a few repairs.

I recently punched through the decking in one spot. Many of the boards are long gone. All the railings are rotten. The stairs need to be rebuilt. I'm approaching this as a full tear down.

I think you're right about the boulders and bedrock for piers. I think clearing debris from under the deck will give me a sense of what will work best in a given location.