Holy water is not shipped in from the Vatican or anything. It is made out of regular tap water by a priest blessing it.
Though Francis performs the symbolic actions of Baptism correctly, the Baptism itself is not valid under current canon law. In order for a non-ordained person to deliver the sacrament, the receiver must be in imminent danger of death and a minister must not be present, of which neither conditions are satisfied. However, this error could likely have been done on purpose to show the irony that a devout Catholic such as Francis does not fully understand Baptism himself.
When Peter decides to be a Mormon, he has 3 wives. The Mormon religion outlawed polygamy (the act of taking many wives) over a hundred years ago (though possibly deliberate since Peter is a moron.)