Job's Suffering: Is God Still Just? Lots of questions in here so I am going to focus on the ~main~ themes/questions I observed.
To begin, God is never proving Himself to Satan, He's already established this. However, God allows the Adversary to test Job so as to demonstrate Job's unfaltering faith in God. God is not directly pulling the strings of suffering, but rather taking a passive seat and allowing such tragedies to fall upon Job.
You ask why God, who is supposedly all-good, to allow such things to happen, especially as it appears as if He is capable of demonstrating Job's faith without the gratuitous pain. This is a great question and one which I feel no one has a succinct answer to, but I will attempt to provide a semblance of an answer,
While the book of Job, upon first reading, may seem like God and Satan pulling the strings of Job's life and thus forcing his hand, it is exactly the opposite. God shows Satan of Job's faith through allowing Him to freely reject or maintain his faith through the trials. Allowing Job the free will to make these decisions is the only way to show Satan that Job is truly faithful and not just "good" because God says it is so.
Next, yes, God does have the foreknowledge of Job's decision making and thus knows from the beginning that Job will maintain his righteousness throughout his trials. This begs the question as to why the trials would even need to occur. With free will, while God knows what path Job will take, he still has the option to take a different path. God is not deciding which path Job will take, that is solely upon Job.
While I do not fully understand why Job, or anyone, must endure such trials I have to believe that there is a greater purpose I am not able to or meant to comprehend (this sucks, I know, still trying to discern why, allllllllll the time). What is evident in the book of Job is God's willingness to let His people suffer in the name of free will, and His ability to remain just in the face of such suffering.
Let me know what you think, this topic and book have been heavy on my heart recently.