Grossdeutchland is interesting, in that it along with Lehr, were the only two army units to receive tigers. The rest went to SS units and the independant heavy tank battalions.
I'm no expert and don't have any of the more recent publications meantioned at the beginning of this thread, but a solid white helmet emblem seems to be origination of this marking. Variations included a white outline only, and with dark yellow vehicles the white marking could be outlined in black fully, or just the top half - (from Panzer Colors III, Bruce Culver).
For the black style, I've only seen it on a Panther from this photo and it has been referred to as a low visibilty marking:
Noticed too that Bison has a few decal sets out that include GD tigers, but no helmet markings are provided for on the sheet nor included on the profile artwork. So no evidence they were used on tigers, but there is always artistic license.
For the barrel question, again I've not seen any official doctrine that called for a different finish. My guess is that in those photos where it appears darker, it is a replacement barrel. It's colour could be, as meantioned already, in primer form that has yet to be painted. It could also be the fact that the vehicle is covered in dust creating that contrast with the new barrel.
regards,
Jack