I know this overlaps a lot of previously asked questions but:
I understand that 'A photon hits a photosensitive molecule in a photoreceptor in the retina, which causes a chemical change. [...] Vision is slow: the cascade in response to a single photon takes on the order of 100s of milliseconds.' (for a persistent perceptual experience, why is video able to have a lower frame rate than audio?)
1) What is the longest amount of time a bright light can shine without it being visible to the human eye? (assume it goes from dark to bright to dark)
2) Would it make a difference if, at other times before and after the bright light, the light was on but dim?
It would depend on the brightness of the light, and that even then it's almost impossible, as it would be to do with the number of photons hitting receptors, rather than how brief a period it happened. (I tried flashing a screen for 1/60th of a second and I could still see it).
I would also guess that the opposite - how long would a period of darkness or dim light have to last in between bright light in order for the brain to not register the darkness - would be much less time, certainly no more than 1/60th of a second. (I tried a 120Hz '3d' screen with glasses producing a 60Hz image).