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Does increasing difficulty also serve to decrease the probability of a 51% attack?
It seems that since difficulty is the same for all, this is not the case. Is that correct?
If difficulty were perpetually at minimum, would the probability of a 51% attack skyrocket?
The dependency goes as follows:
The difficulty depends on the total hashing power. As the hashing power goes up, so does the difficulty. This is intended to keep the block generation rate roughly constant at about one block every ten minutes.
As the total hashing power goes up, so does the amount of hashing power needed to accomplish a 51% attack. The total hashing power is the thing you need to accumulate 51% of.
So there is a direct relationship, but it's because they're both directly tied to total hashing power.
@DavidSchwartz' answer, covers most of the question, but to address the last point:
If difficulty were perpetually at minimum, would the probability of a 51% attack skyrocket?
A very low difficulty would increase the probability of a majority attack. This would not be a direct effect of the difficulty, but indirectly due to the time required for block-propagation. At a very low difficulty, the party with the highest hash-power would be able to churn out a lot of blocks quickly and could immediately start building on top of those again, while other miners would be hampered by the block propagation latency.
