Can the status of a Muslim son precede that of his father in Paradise, and are the good deeds of his children recorded for the father, which would prevent any of them from surpassing him?

It is not impossible for the son to precede his father in Paradise if his deeds are better, for every soul is recompensed for what it has earned. The son's good deeds are not credited to his father, for Allah Almighty says: "And that man will not have except what he endeavored for." And what a person endeavors for includes what he was a cause of, such as guiding to good and raising well.