What is the ruling on the prayer of one who led the prayer (as imam) while not in a state of ritual purity (wudu'), and must he repeat the prayer for those who followed him (the congregants)?

You did well in repeating the prayer you performed without ablution due to forgetfulness. As for the prayers of those who prayed behind you, their prayers are valid according to the majority of scholars, and deputizing someone else to pray on behalf of another is not prescribed in prayer.