The grace bestowed in Baptism does not depend on the state of grace of the priest or deacon, but only depends on the form of the Sacrament. If they before what the Church calls for, then the Sacrament is valid.
It's not about "getting the child's head wet," but the form plus the matter. "I baptize you in the Name of the Father, and of the Son, and of the Holy Spirit," while pouring water over the person to be baptized, is all that is needed. In emergency situations, any Catholic or Orthodox Christian can baptize.
Where does the baby go? There is no limbo any longer.
How can an unbeliever be saved by sprinkling water on it's head? That isn't in God's Word.