They have indeed received the Great Commission. Right at the end of The Gospel of Matthew:
Mat 28:19-20 Therefore go and make disciples of all nations, baptizing them in [fn] the name of the Father and of the Son and of the Holy Spirit, and teaching them to obey everything I have commanded you. And surely I am with you always, to the very end of the age."
Unless one has received the laying-on-of-hands (aka Holy Orders) through apostolic succession, then one does not have any authority to preach the Gospel, it is that simple.
Incorrect. No such direction is given. In fact, Jesus told His disciples:
Luk 9:49-50 "Master," said John, "we saw a man driving out demons in your name and we tried to stop him, because he is not one of us." "Do not stop him," Jesus said, "for whoever is not against you is for you."
That is a failed attempt at interception. It was not thrown to them and they did not catch it. Christ was addressing His gathered apostles and disciples, the bishops and priests of the Catholic Church.
His disciples received Holy Orders...directly from the Apostles at/after Pentecost...Jesus only ordained the twelve. But all priests can trace their ordination back to the twelve.