What is the ruling on the prayer of the imam and the congregants, and is the imam sinful, if he completes his prayer as an imam after passing wind in the first rak'ah, and does not appoint a successor due to his knowledge of the congregants' ignorance of the ruling, then repeats his prayer alone without informing them?

You committed a great error by continuing to pray while being in a state of ritual impurity (hadath). Your prayer is invalid by the unanimous consensus of scholars. The fact that the congregants are not students of knowledge is not an excuse for you. Rather, you should have stepped back and appointed someone else to lead. You must seek forgiveness for what you did. As for the prayer of the congregants, the more preponderant opinion is that it is valid, because they were unaware of the Imam's state of ritual impurity.