Okay, I'm no expert on doppler shift with light waves but here's what I think:
a.) is your correct answer.
b.) light (photons) do not age. To age is to change over time. For photons of light, traveling at the speed of light, time does not exist for them. Things age outside of the photon in a different reference frame. Remember that Special Relativity says that for any two reference frames moving "linearly" with respect to one another, there are no unique frames of reference, that each reference frame has the right to claim that they are not moving but the other reference frame is moving, etc. From the photon's reference frame, time stands still -- it is everything else that is moving and aging.
c.) this one is a little tricky but again, one has to ask in what reference frame is the photon wavelength stretching? "... the wavelengths of the photons are stretched while they trave through [the expanding space]. No, the photon wavelength appears "stretched" (red shifted) from the observer -- in a different reference frame. Not in the same reference frame as the expanding space in which the photon is traveling.
d.) Well? Under some very restrained conditions, there may be some physics to support this idea. But for this question/problem, d.) is wrong.