How do you even carve the details of the ice to the point that it has different shades

...maybe reflecting light?

Have you ever seen any ice sculptures that can reflect light so perfectly to form eyes like those

Nope ^^

How you do it is carve into the eyes. darker it is, more it recesses. So the shine of the eyes is on the outside, and each darker shade is further in. Probably the shine of the eye has been textured so that it doesn't have an actual shiny surface, and looks like snow.
https://kathyoconnellsart.files.wordpress.com/2011/07/eye-plate.jpg
It might be harder with ice's transparency, but that sculpture did not look transparent.

wooow ヾ(☆▽☆)