Is it permissible to use the word "mudabbir" (مدبر) for other than Allah, such as when a person says: "I will manage (mudabbir) tomorrow such-and-such an amount of money," or "Manage (dabbir) such-and-such an amount of money for me"?

There is no objection to applying the word "tadbir" (planning/management) to other than Allah Almighty, for its linguistic meaning is to consider the outcome of a matter and to act upon it after careful thought and deliberation. There are hadiths that mention the virtue of "tadbir," but they are weak.