Is it a condition for divorcing a wife who married customarily without her family's knowledge that the marriage first be formalized legally and then the divorce occur, or is the divorce valid simply by the husband saying: "You are divorced"?

The majority of scholars hold that marriage is not permissible without a guardian (wali). Therefore, your marriage without your parents' permission is invalid, and the preponderant and authoritative opinion is that of the majority. This marriage must be annulled immediately, and you must hasten to repent and distance yourself from this husband. It suffices to separate from him by a divorce initiated by the husband or an annulment by a judge. The children are legitimate and belong to him. You can marry him again by fulfilling the pillars of marriage (a guardian, two just witnesses, a dowry). The marriage is not annulled if a Sharia judge rules it to be valid. If your father refuses to marry you to a man who is legally competent, you may refer the matter to a Sharia judge to marry you or order one of your guardians to do so.