Does a divorce occur with the conditional phrase: "You are divorced if something happened between you and that young man that you are hiding from me and have not told me about"? And is it obligatory for me to confess to my husband what happened, or is it permissible for me to remain silent, and would I be sinful if the divorce occurs and I do not confess to him?

This sin began with conversation with a non-mahram (definition) man and then developed, and it is forbidden. If your husband has conditioned your divorce on you telling him what happened, then either you tell him or the divorce will occur, and you will become unlawful to him after the waiting period unless there is a new marriage contract. You have two options: tell him the details and bear the consequences, or tell him that you have concealed some matters and will not disclose them. In the second case, the husband knows that divorce has occurred, and the choice remains his whether to take you back or separate, without you having to fully expose yourself. We advise the second option, informing him that the details of what happened are a secret between you and Allah, and that you have repented from it, and he has the choice to keep you or divorce you while maintaining discretion.