The difference between a mirror operation and a glide operation is that the latter is followed by a translation of half a unit cell, i.e. a few Angstroms at most. If you want to describe, say the refractive index and your wavelength is 500nm or 5000A (green light) do you really think that tiny...
Well, they are all two-fold axes. So, which one you choose to be the unique z-axis is really up to you. In groups like D_3 D_4 that is not so because one is a three- or fourfold and perpendicular to that you have twofolds. So then you should pick the higher order axis to be the main z-axis.
''Since there is no difference between k and k-G in term of energy does that mean that they are the same state?''
In general a point k and the point k-G (or k+G or k+2G etc.) represent different wave functions with different frequencies and different energies, but they all belong to the same...
Do you mean the group D_2?
There are three B irreps there. I think because it is not clear what the principal rotation axis is: the three axes are equivalent.
To study the properties of your system you might want to apply a bias, but means that you have to supply it.
The idea of a solar cell in real operation is to obtain energy from it, not supply to it. So there you generally don't want to have to apply a bias.
I believe diamond's space group is Fd3m that is F4sub1/d -3 2/m, not Fm3m like NaCl-type
This is a non-symmorphic space group: it has fourfold screw axes and diamond glides: symmetry elements that combine rotation with partial translation. For some properties like optical ones that does not...