1. With only one exception I can think of, every instance of insomnia I've had in the last several years I can trace to not having f.lux enabled for some reason.
2. The reason that happens is that I often won't notice if f.lux dies for some reason, because I am so thoroughly used to it now.
I was having real sleep trouble several years ago, and f.lux is part of a battery of things I did (along with cutting caffeine completely after 12:00PM every day, getting some aerobic exercise, not coding after ~9:00PM, and taking over getting the kids out the door in the morning to force myself to get up) which more or less eliminated those problems.