The image on the retina is not symmetrical, though. Try to exploit any apparent symmetries and you'll end up smearing/distorting/destroying the image you're trying to convey.
Four dimensions to specify a ray: two dimensions for direction, and two dimensions for where it passes through the surface (whether the surface is the display, or the viewer's eye). You could specify a ray with five dimensions (three spatial, two angular), but that's actually overdetermined; any ray with the same direction along the same line is identical, so it's a four-dimensional quantity. (Source: I do this for a living. But google 'plenoptic function' for more technical explanation.)
Those four dimensions are projected into two on the retina, but the exact projection is a function of where the person is focusing. (That's how we understand focus; by changing the lens parameters, we can focus at different depths in the scene.)
Yes, but it doesn't matter if the ray is going up or down or left or right, as long as the angle from the normal is the same. This is because the lens in the eye is circular, and the image that results on the retina is the same.
So three dimensions:
two for position and one for "amount of off-axisness".
