Mark.06 is black (some kind of very dark green or something), it just wears some kind of white "clothes". As for the mask it's probably removed when they put the helmet in place. It's an Adam.
Actually, they made holes in the mask and the helmet was installed on top of it :
[wkimg]Eva2-22 C0304 mark06.jpg[/wkimg]
Strangely, the big hole in the upper right side of the mask is symmetrical to another one on the left side of the mask, and these two holes were already here when it was just excavated at the end of 1.0... could that mean that this ADAM was already wearing something on this head that got ripped off when it was ejected to the Moon?
This is a metamorphic all-core thing, probably the same "Vessel of Adams" as 09. if Adam's body is not equivalent to "Vessel of Adams", one possible explanation that they converted Adams's body to that thing and used this autonomous unit to hibernate Lilith. Anyway, it was necessary convert embryo appeared from the remnants of Lilith into the core (which should possess Lilith's fruit of wisdom), and this all-core angel was probably necessary exactly for this purpose.
In a story-board in the 2.0 CRC, it's revealed that during 2I a giant spurt of blood erupted from the center and left that giant bloodstain on the Moon, since the Giant and the Spear were excavated from a place of the Moon covered by the giant bloodstain, we can safely assume that Mark.06 is one of the four ADAMs and got ejected to the Moon with the LoC during 2I.
Because it was awakened by the core from 00, their cores should possess different fruits. As in the original show, 01 probably is made from the half of Lilith.
It seems that impact requires presence of two cores of different fruits to make a "god-like" or FAR-like being (which is able to open a Guf-door), and pilot's emotional burst.
Actually, it was awakened by Zeruel's remains that coalesce around Unit-00's core, forming the "Giant Naked Red Rei" that EVA-01 absorb.
So EVA-01 absorbed Zeruel's FoL. That would support the theory that its made from Lilith, like in NGE... but it also absorbed Rei at the same time, and if she possess a Fruit of Knowledge(and without taking into account that she may have Lilith's soul like in NGE), that could mean that EVA-01 is actually one of the 4 ADAMs, the fact it seems to have a third eye that appeared when it gecame a giant of light also support that theory.
As for EVA-13, it was outright stated that it was one of the four, but we're not sure if what awakened it was the fact it ate the 12th Angel or because said 12th absorbed Lilith's remains prior(when it morphs into a giant red fetus, you can see it begin when it make contact with the liquefied remains of Lilith, and the fact it briefly morphs into a giant Rei head and that later multiple Rei heads appears on it support that theory).
So in the end Unit-01 could be from Lilith or one of the four surviving ADAMs.
Usually I act in parallel with the original, you may accept anything I write as a speculation. In the original it was in the mask of FAR (craters on the mask were definitely from unsuccessful landing), here she may be in the mask of FAR by analogy.
As it was already mentioned, FAR is logically necessary, or NME is a kind of techno-fantasy.
The mask of the giant in the Moon bears the same kind of damages that Lilith's mask in NGE, suggesting that it may always have been on his face and not added by SEELE.