Is a conditional divorce, made with the words "if she gives up her rights, I will divorce her," annulled after reconciliation, and does this conditional divorce revert if a dispute occurs months later, knowing that the intention was not an immediate divorce but contingent upon her waiving her rights?

This phrasing ("If you waive, I will divorce her") does not result in divorce merely by the woman waiving her dowry. Rather, it is a promise of divorce. Therefore, if the woman waives her dowry based on this promise, the divorce does not occur, and the man is not obligated to divorce her, because a promise of divorce does not necessitate fulfillment.