p-n junction

The barrier potential depends on the semiconductor material (about 0.7 V for Si and 0.3 V for Ge), on the amount of doping and on temperature.
So all three factors (a), (b) and (c) matter.

In forward bias, the positive terminal of the battery is connected to the p-side and the negative terminal to the n-side.
The applied voltage opposes the barrier potential, so the effective barrier height is reduced.
Majority carriers are pushed towards the junction, which reduces the width of the depletion region.
Connecting the positive terminal to the n-side is reverse bias, in which the depletion region becomes thicker.
Hence in forward bias the positive terminal is connected to the p-side and the depletion region becomes thin.