@sarahjamielewis Fantastic starting point, thank you for writing this up!
Regarding proof that someone indexed an authentic HTTP response, I had thoughts on that a while ago, though I'm not sure my idea is practical for this (or any) use: https://jamey.thesharps.us/2020/06/13/authenticating-shared-web-caches/
I love that you cover query privacy and the desire to do ranking locally. I mentioned yesterday that I'm interested in using data from my local history and bookmarks during ranking and wouldn't want to send those elsewhere, and it sounds like you're on the same page for other reasons.