Is the son of Adam predestined or free-willed, and how does one die if the Throne of the Most Merciful trembled at his death, and does this mean that God did not know of his death?

If "Bani Adam are controlled by Allah" means that they are compelled without will, then this is false; because Allah has affirmed will for the servant, as He says: "So whoever wills may take a path to his Lord." But if it means that the servant's will is subordinate to Allah's will, then this is true, as He says: "And you do not will except that Allah wills."

And if "he has freedom" means that man has choice and uncoerced will, then it is correct. But if it means freedom outside the dominion of Allah, then it is false.

As for the trembling of the Throne of the Most Merciful at Sa'd's death, it does not mean Allah's lack of knowledge, but rather joy at the arrival of his soul and Sa'd's great stature in Islam. The questioner is advised to use Islamic terminology in matters of creed.