Diffusion current
When a p-n junction is formed, a diffusion phenomena causes electrons from the n-doped region to diffuse to the p-doped region. At the same time (even if it's an abstraction) holes diffuse from the p-type region to the n-type one. The atoms that lose a carrier (electron or hole) become ions, which means that instead of being neutral, they have a positive or negative net charge. This happens because the ideal equilibrium would have the same concentration of mobile carriers equal all over the region.
Ohmic current
However, this diffusion causes the growth of a region, populated by ions, called depletion region, because all atoms have lost their carrier. These ions, as we said, are electrically charged, and cause an electric field directed from the n-region to the p-region, pushing carriers in the opposite way than diffusion. Therefore an equilibrium is reached in which the current (movement of carriers) caused by diffusion is perfectly balanced by the current caused by the electric field (ohmic current).
Effect of biasing
Applying a potential to the junction causes a perturbation on this equilibrium, making one of the currents dominant on the other. Reverse biasing the junction causes the ohmic current to prevail, while forward biasing increases the diffusion current.
Now, the diffusion current is a much stronger phenomena, from which derives the exponential growth of the forward bias current with the bias voltage. Ohmic current, on the other side, is much weaker, and saturates quite soon (neglecting avalanche effect) because the width of the depletion region (which determines the resistivity) is proportional to the reverse bias voltage.
Does electric potential influence the direction of current?
Yes it does. As you said, conventional current flow is from a higher potential to a lower one.
With your typical AC waveform (a sinusoid), the voltages don't switch discretely. They gradually increase or decrease. For one half of a cycle, one terminal will be higher than the other, and you will have current flow from the more positive to the more negative. For the next half of the cycle, the other terminal will be higher, and you will have current flow again from whichever terminal has a higher potential relative to the other. This is conventional current flow.
Best Answer
There's a little backstory here.
Conventionally, the direction of current is from positive pole to the negative pole, though the actual direction of electrons is from negative to positive as in the image.
The term 'holes' is used in this circuit just because silicon is a semiconductor, which means it can have characteristics of both conductors and insulators. Holes are a term given to absence of electrons. The holes do not move by themselves. But, yes, holes appear to be moving in the opposite direction to electrons, when the electrons in the semiconductor device move from one vacancy to the another.
Hence, here you can say the direction of the current is the direction of the holes!
Yes. With a sufficient amount of kinetic energy (applied voltage), the valence electron of one atom moves out and occupies the hole in its adjacent atom; consequently creating a hole in the atom which the valence electron left. This goes on and appears as if the holes are moving.
This sounds peculiar at the beginning, but as you proceed to learning pn-junctions and diodes, you'll gain a better insight.
Let me know if I cleared you.