Pardon me - I'm having difficulty getting this entire reply posted - even editing/adding bit by bit isn't working now, so I'm continuing with a second post.
As for Galadriel making the rope, I think everyone is remembering Sam's comment in The Taming of Sméagol:
Quote:
'It goes hard parting with anything I brought out of the Elf-country. Made by Galadriel herself, too, maybe. Galadriel,' he murmured, nodding his head mournfully. He looked up and gave one last pull to the rope as if in farewell.
To the complete surprise of both the hobbits it came loose.
...
'but I think the rope came off itself - when I called.'
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By calling Galadriel's name, did Sam 'activate' the 'magic' in the rope? Note how Frodo tries to find more logical explanations. Maybe the knot held as long as there was sufficient tension on the rope. Once they were down, the silky rope relaxed and recovered, loosening the knot. Rope with memory. A great bit of technology. Or subtle magic.