Great question — answering as the UphillTech team:
To answer just question 2, a very long extension cord should not trip a GFI. If it's damaged, cracked through the outer and inner insulation, that might do it. If its indicator light is leaking to ground, that could also do it and that might be intermittent since its normal power might be below the GFI's threshold. The extension cord is no different to all your string lights. If there is an actual ground fault in it, that would be a cause. You seem to have eliminated it in experiment 3.
Full answer by jay613: https://diy.stackexchange.com/a/288482 (CC BY-SA 4.0).
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