What should a young man do who wants to buy a car for work and marriage, while his mother refuses out of fear for him from accidents, even though he has told her that everything is by divine decree and destiny?

You are not obligated to obey your mother if her refusal to buy you a car is merely out of pity, as that is not a valid justification, and you are not required to obey her in this instance. It is advisable to continue trying to convince her and to seek another means of earning a livelihood.