What is the smallest visual unit perceptible to the human eye, like a pixel? (esp. in visual static)
The human eye has two types of sensors that become stimulated when wavelengths of visible light (photons) hit the pigments in these sensors. They are known as 'rods' and 'cones'. Rods detect the brightness of light, cones detect the color. There are three different cones in the human eye: red, green and blue. Each cone reacts to the corresponding waves of light. When they are stimulated due to their corresponding wavelengths, they send a signal that travels through the optic nerve to the visual cortex at the occipital lobe.
individual cones don't have different levels of stimulation and always send the same frequency, it's the lack of the stimulation of other cone types that causes certain colors to appear.
in short:

signal or photon of the appropriate wavelength I suppose.
rods for brightness, cones for color.
probably not since the cones are microscopic and tightly packed, too close and too small to see what each cone is literally receiving. The moving static you're seeing is called phosphenes and is comprised of the inherent electrical charges the retina produces both during resting state and with the eyes open. they're just easier to notice when your eyes are closed. Try covering your eyes and you may get static just like when you close your eyes.

The electrical charges get sent to the visual cortex. that's where your brain processes the image. Here's an diagram of how the rods and cones send their electrical signals to the optic nerve (the optic nerve is the [4] label).

Here's a diagram of how those signals travel to the visual cortex: