No light but hot wire is hot
You have an open neutral somewhere in the line

From the meter readings you took with the breaker off, namely no continuity between any pair of wires, even neutral to ground which should have a low resistance between them since they are connected at the main panel, as well as the neutral "ringing" as hot with a non-contact voltage detector, it sounds like you have an open neutral somewhere.  I would go down this circuit from the failed point towards the beginning, replacing failure-prone backstab connections into receptacles with proper shepherd's hooks around the side-screws instead, and making sure there isn't a failed wirenut splice somewhere, either.