The human eye can't detect single photons. However, it can detect a few simultaneous photons at the retina, which corresponds to a hundred or so entering the cornea.
Sort of. This is from memory, but here's how I remember that experiment working:
In that experiment, they showed that, for some value of n, rod cells consistently activated in response n photons, and did not activate in response to (n-1) photons. Thus, they argue, rods are sensitive to single photons.
In some sense, they're right, in a straw that breaks the camel's back sort of way. However, the common mis-interpretation of these results is that n=1; that is, in utter darkness a rod cell would fire in response to a single photon. But this is not what the experiment showed.
(Note that just because a rod cell activates doesn't mean that the organism would perceive light. In order for a signal to reach the optic nerve, a retinal ganglion cell needs to activate. Ganglion cells only activate in response to the activation of a significant number of photoreceptors. Only in some part of the fovea, where there are no rods, is there a 1:1 mapping of photoreceptor to ganglion cell. In most parts of the retina the ratio is closer to 1 ganglion cell per 100 photoreceptors. Furthermore, even if a ganglion cell activates and a signal reaches the optic nerve, that still doesn't mean that the organism will perceive light. It's likely that further levels of processing may filter out transient activations.)