Q. 1. Can you tell me who can administer the Sacrament of Baptism?
A. 1. On this matter, the Canon Law of the Catholic Church states:
Chapter II : THE MINISTER OF BAPTISM
Can. 861 §1 The ordinary minister of baptism is a Bishop, a priest or a deacon, without prejudice to the provision of can. 530, n. 1.
§2 If the ordinary minister is absent or impeded, a catechist or some other person deputed to this office by the local Ordinary, may lawfully confer baptism; indeed, in a case of necessity, any person who has the requisite intention may do so. Pastors of souls, especially parish priests, are to be diligent in ensuring that Christ’s faithful are taught the correct way to baptise.
Can. 862 Except in a case of necessity, it is unlawful for anyone without due permission to confer baptism outside his own territory, not even upon his own subjects.
Can. 863 The baptism of adults, at least of those who have completed their fourteenth year, is to be referred to the Bishop, so that he himself may confer it if he judges this appropriate.
In other words,
In a case of an emergency, anyone can administer the Sacrament of Baptism, providing there is an intent to do so and the proper words are being said.
Excluding the aforementioned, under normal circumstances, only a Bishop, a priest or a deacon can administer the Sacrament of Baptism within their territory (parish).
The Bishop reserves the right to baptize those who have completed their 14th year.