We will have the following:
A. Other factors that would affect the acceleration of a falling object would be the medium it is falling trough and external forces.
B. Yes, it all comes down to the way external forces act upon the object, since the laws of physics will remain the same, as far as current knowledge of the universe indicates. Also the medium will play a roll as well, this is mainly due to the nature of the fluid it is traveling trough, that is density and such.