If we look at a galaxy, say 100 million ly away, we are seeing a picture of what that galaxy was 100 million years ago. So, when in a year, this galaxy has moved (100 million + x ) ly away, would we seen a picture (100 million + x) years ago?

Yes, but the difference would be fractional.  Without doing the sums, I would guess at a few seconds per year.    Note also that galaxies have their own motion as well as sharing the general expansion of the universe.  We are actually drawing closer to the Andromeda Galaxy and a merger is expected.  All galaxies in the Virgo Supercluster are gravitationally bound and so will stay together even when expansion has widely separated our supercluster from others.

No, since in that year we have aged 12 months as well we are still seeing the galaxy as it was 100 million years ago. Expansion of the universe etc is negligible over a period of time shorter than a year.

I'm not an astrophysicist and I hardly know anything about relativity and or special relativity. But according to my common sense, here is what I inferred from this wikipedia page http://en.wikipedia.org/wiki/Speed_of_light : Since the speed of light is independent of the wave source and the inertial frame of reference of the observer. Also, the speed of light is isotropic i.e. its value doesn't change by changing the direction from which it is measured. Hence, the time taken by light to reach us from a star at (100 millions + x) light years will take (100 millions + x) years to reach us from the time it was emitted. http://en.wikipedia.org/wiki/Speed_of_light#Fundamental_role_in_physics Now would we be able to see the galaxy 100 millions + x years ago depends on the value of x. I'll use propagation of light as a wave-front to explain this part. http://en.wikipedia.org/wiki/Wavefront Since light travels in the form of wave-fronts and considering very large distance between the star and the earth, we can assume the star to be a point light source. So the wave-fronts are spherical wave-fronts. Now as wave-front travels further, the size of wave-front increases and so does the distribution of energy in the 3-D space. If x is extremely large then it would be hard for us to notice any light waves as there will be extremely low amount of energy incident on the receivers. So we will need receivers of extremely large apertures which might not be feasible to install. Now if x is small and we can detect the light waves received from that star, then it's possible to monitor the velocity with which it is moving away has been reduced or increased by doing the spectral analysis of the light waves and measuring the redshift. http://en.wikipedia.org/wiki/Doppler_effect#Astronomy