I'm not sure but I think there are human albinos with blue irises, which would mean their eyes do produce some melanin, since that's what makes the blue color in human eyes. I haven't looked at a lot of butters, but I'd assume they could have the same thing, plus they're producing lots of yellow and red, so I could see how their irises would be something other than pink. (?)
As for the "hall of mirrors" effect, I figured a quick visual would make more sense of it...
At some point on TV or in a movie I'm sure you've see where the camera pans across a bright light source (like the sun), and you see these little circles or hexagons that swipe across the screen like a windshield wiper.
If you follow one light ray you can see what happens more easily... it normally goes in through the camera lens and through the shutter and into the camera, but when there's a bright enough light, enough of it actually reflects off of the inner lens, or whatever inside the camera. Since the camera is not pointing directly at the light source, it starts heading back out toward the open again, but at a bit of an angle. At the correct angle, this light hits the inside of the shutter (or is it the back of the lens?) and bounces back at the camera lens again. Each of those little hexagons or circles you see on the screen are one reflection of light coming back into the camera. (This is why they also go in a straight line across the screen.)
With an eye, the same thing can happen. Normally melanin is present on the inside of the eyeball so that light doesn't bounce around, which is why your pupils are black. Normally light passes through the lens and is focused on the retina. Say you were in the dark looking at a blue flashlight and a green flashlight which were pointing at you:
Based on where the light hits, the brain figures out where it's coming from.
Here's an example of what I'm talking about with the "hall of mirrors" effect. With even just one flashlight, if the light bounces around inside your eye, you could see what looked like a bunch of green lights:
How many reflections you'd see would depend on how easily it bounces around, and how weak the light has to get before you cannot see it anymore. I guess the best way to answer that question would be to try that with a human albino who could tell you what he's seeing.
The other problem albinos have is that the light, if it's bright enough, can just come right through the iris, and so a lot of "extra" light is coming into the eye and getting scattered all over. Below is light coming from the same source that ends up hitting two spots on the retina.
I'm not really an expert on this, but that much of it is pretty easy to follow along with, even for me. Hope it made sense for those who were scratching their heads.