Does the money I gave my father become his property, and is the Zakat obligatory upon him or upon me, especially if I later ask him to buy something expensive with this money, knowing that my primary intention was for the money to become his property?

If you donate money to your father and he takes possession of it, the money leaves your ownership and transfers to his. You are not obligated to pay zakat on it unless a full year passes while it is still in your possession. Zakat becomes obligatory upon your father if a full lunar year passes after it enters his possession, provided the money reaches the nisab (minimum threshold). A gift becomes binding upon possession, and it is not permissible to revoke it. The money does not revert to you simply by your words. You can receive from your father the price of the item you wish to purchase, if he agrees to it.