Regarding eNotes guidelines, editors may only answer one question per posting. Therefore, I will address what I feel to be the most important question you have asked.
"Is nature really unjust in "The Open Boat"?
The answer to this depends on your train of thought in regards to what is considered unjust. Nature simply does not have the mental capability to decide to be unjust. Nature is simply a force which exists and all affected by it must deal.
Traditionally, Naturalistic literature focuses on the power of Nature over man. Man lacks free will in most Naturalistic pieces (while they typically are unaware of this). Therefore, man can only be a piece in the grand scheme of things.
The situation in "The Open Boat" is no different. The men are at the mercy of the sea. The sea, here, is all powerful. It is only through Nature's mercy (forgive the personification given I previously stated that Nature does not "do" anything, it just "is") that the men survive.
In the grand scheme of things, Naturalistic texts focus on the survival of the fittest (influenced by Herbert Spenser and Darwin). Here, the men survive, but not because they are stronger than Nature. Instead, they survive (perhaps) because Nature is finished toying with them.
So, to make a concise answer to the question: No, nature is not unjust--it simply exists.
[Note the use of Nature (given its capitalization) as an entity- this is done because of how Naturalistic writers gave power to nature].