I have a question in regards to baptism: Was baptism authorized after Jesus' death or while Jesus was walking on earth? Please, could you provide clarification?
After discussing with Nicodemus about the necessity of being born again of water and the Spirit, which alludes to baptism, (John 3:5), we find that Jesus left and began baptizing disciples. "After these things Jesus and His disciples came into the land of Judea, and there He remained with them and baptized" (John 3:23). A bit later we learn that the baptisms were actually done by his disciples, but since they were done with Jesus' authority, they were his baptisms. "Therefore, when the Lord knew that the Pharisees had heard that Jesus made and baptized more disciples than John (though Jesus Himself did not baptize, but His disciples), He left Judea and departed again to Galilee" (John 4:1-3). Notice too that these baptisms were not the same as John's, that is, they were not done for the same purpose. Those who were baptized with Jesus' baptism became His disciples. This became a point of contention between John and Jesus' disciples. "Then there arose a dispute between some of John's disciples and the Jews about purification. And they came to John and said to him, "Rabbi, He who was with you beyond the Jordan, to whom you have testified--behold, He is baptizing, and all are coming to Him!"" (John 3:25-26). John then explains that this was what was supposed to happen.
Some will ask when were the apostles baptized and these same passages explain it.
A few people have difficulty with the idea that New Testament baptism could take place before the New Covenant was executed by Jesus death. But there really is no conflict except what is imagined. I might leave one of my children a favorite heirloom in my will, but nothing is out of place if I decide to give that heirloom to him before my death. Circumcision was a required sign of the covenant under the Old Testament law (Leviticus 12:3). Yet the Lord required it of Moses' children prior to the giving of the Law (Exodus 4:24-26). And, the first Passover meal (done before the covenant was made at Sinai) required all males to be circumcised. "For no uncircumcised person shall eat it" (Exodus 12:48). People can begin following the terms of a covenant prior to its official start date.