Re: In mirrors, does a relection of a reflection retain it's 3-d depth?

A reflection of a reflection doesn't have any fundamental effect on
the image, but it is certainly true that all mirrors are imperfect
to some degree so the more reflections the more the imperfections
come to dominate.  You can see this in some clothing store fitting
rooms where one mirror faces another one and is parallel to it.
Here you can get an impression of "looking into infinity", although
you'll generally find that the "distant" images generally look dark
and increasingly distorted.

When trying to look at your own head from the side using mirrors,
it's probably also true that the exact angle and distance (the
path length) from head to eye can lead to different appearances
of shape.

In terms of the appearance of 3D depth, the most important factor
is likely to be whether both eyes get a good view of the reflection:
if they do, then stereoscopic vision allows you to perceive 3D, if
one eye sees the reflection poorly, or not at all (often the case
when trying this sort of thing), then the reflection will indeed
look flat.