Are the teachers and prophets who laid hands on Saul & Barnabas in Acts13:1-3 ordained Bishops?
It is not impossible that Paul could have been ordained a priest in Acts 13:1-3 and consecrated a bishop by St. Peter in Galatians 1:18.
The ordination of bishops belongs to the Apostles and their successors. Teachers and Prophets can not ordain priests or consecrate bishops.
The ordinary minister of the sacrament is the bishop, who alone has this power in virtue of his ordination. Holy Scripture attributed the power to the Apostles and their successors (Acts 6:6; 16:22; 1 Timothy 5:22; 2 Timothy 1:6; Titus 1:5), and the Fathers and councils ascribe the power to the bishop exclusively. First Council of Nicaea (Canon 4) and Apostolic Constitutions VIII.28 — "A bishop lays on hands, ordains. . .a presbyter lays on hands, but does not ordain." Holy Orders (Catholic Encyclopaedia)
Thus the short answer is no.
13 Now there were in the church which was at Antioch, prophets and doctors, among whom was Barnabas, and Simon who was called Niger, and Lucius of Cyrene, and Manahen, who was the foster brother of Herod the tetrarch, and Saul.
2 And as they were ministering to the Lord, and fasting, the Holy Ghost said to them: Separate me Saul and Barnabas, for the work whereunto I have taken them.
3 Then they, fasting and praying, and imposing their hands upon them, sent them away. - Acts 13: 1-3
I can find no historical proofs or traditions to back up the statement of an episcopal ordination here. There is nothing to indicate that any of the persons mentioned in in Acts 13:1-3 were even considered bishops in this passage, at this precise moment in time. Teachers and prophets are not bishops!
27 Now you are the body of Christ, and each one of you is a part of it. 28 And God has placed in the church first of all apostles, second prophets, third teachers, then miracles, then gifts of healing, of helping, of guidance, and of different kinds of tongues. 29 Are all apostles? Are all prophets? Are all teachers? Do all work miracles? 30 Do all have gifts of healing? Do all speak in tongues? Do all interpret? 31 Now eagerly desire the greater gifts. - 1 Corinthians 12: 28-31
Thus the Apostles and bishops are not of the same status as teachers and/or prophets!
Many Protestants, and I’d guarantee some Catholics, think that St. Paul became an apostle on the road to Damascus when he was struck down, when Jesus spoke to him and converted him: “Saul, Saul, why are you persecuting me?” Since this happens in Acts 9, and the Council of Jerusalem happens in Acts 15, it seems like the time line is very short. But we know that Paul, after the scales came off of his eyes in the home of Ananais, and had recovered his strength, he preached in Damascus, so strongly that the Jews desired to kill him. He was lowered in a basket to escape, and Barnabas took charge of him in Jerusalem-this was his first meeting with the apostles, but they were wary of him. After another plot to kill him was discovered, they sent him to his home town of Tarsus. Acts then shifts the scene to Peter, but what of Paul?
The answer is in the book of Galatians. Galatians 1, after Paul’s introduction, verse 13, Paul says “You heard about my former actions in Judaism”, then gives a timeline-he says he did not go back to Jerusalem ‘to those apostles who were before me, rather I went into Arabia and then returned to Damascus. After three years he went up to Jerusalem to confer with Cephas, Peter, and stayed with him for 15 days, not seeing any of the other apostles. Then he went to Syria and Cilicia, and was unknown to the churches of Judea. Chapter 2 starts off “After 14 years…and presented to them the gospel I was preaching. Verses 7-9 is when the apostles “recognized the grace bestowed upon me”, “gave me and Barnabas their right hands in partnership, that we should go to the Gentiles and they to the circumcised.”
This is when Paul became an apostle. To recap, he was converted (not his own word), went into the desert, then after three years went to Jerusalem, then after 14 years, he went back to confer with the apostles, at which time they laid hands on him, which is really when Paul becomes an apostle.
This shows a couple of things…it shows clearly what Paul demonstrates in the letters to Timothy about what is required to be a bishop, a successor of the apostles. It requires laying on of hands. Secondly, it shows how we must sometimes reconstruct the way things happened-piecing together what we know in order to figure out things that aren’t so readily apparent. Third, it shows how the Catholic Church is really the Church Jesus founded. - When and how did St. Paul become an apostle?
In Galatians 1:1 St. Paul simply declares he is an apostle and he is thus sent from God and not men to preach the Gospel.
1 Paul, an apostle—sent not from men nor by a man, but by Jesus Christ and God the Father, who raised him from the dead, and all the brothers and sisters[a] with me. - Galatians 1:1-2
In fact the full answer lies further down in Galatians 1, when St. Paul meets St. Peter (Cephas) in Galatians 1: 18. This is where he is ordained an apostle by St. Peter himself. Saint Peter, also known as Simon Peter, Cephas, or Peter the Apostle, was one of the Twelve Apostles of Jesus Christ.
18 Then after three years, I went up to Jerusalem to get acquainted with Cephas and stayed with him fifteen days. 19 I saw none of the other apostles—only James, the Lord’s brother. 20 I assure you before God that what I am writing you is no lie. - Galatians 1: 18-20
Although this is taken as to when The Apostle St. Paul was raised to the dignity of an apostle and bishop; the actual episcopal ordination of St. Paul is nowhere found in Scripture. It remains part of Sacred Tradition.
Thus to get the full gist of what St. Paul is truly saying in Galatians 1:1, we must read the entire chapter carefully and take it as a whole. It is to be understood in it’s integrity.
The Apostles and Disciples of Jesus accepted St. Paul and St. Barnabas were welcome amongst the Apostles in Galatians 2: 2-10.
Paul Accepted by the Apostles
2 Then after fourteen years, I went up again to Jerusalem, this time with Barnabas. I took Titus along also. 2 I went in response to a revelation and, meeting privately with those esteemed as leaders, I presented to them the gospel that I preach among the Gentiles. I wanted to be sure I was not running and had not been running my race in vain. 3 Yet not even Titus, who was with me, was compelled to be circumcised, even though he was a Greek. 4 This matter arose because some false believers had infiltrated our ranks to spy on the freedom we have in Christ Jesus and to make us slaves. 5 We did not give in to them for a moment, so that the truth of the gospel might be preserved for you.
6 As for those who were held in high esteem—whatever they were makes no difference to me; God does not show favoritism—they added nothing to my message. 7 On the contrary, they recognized that I had been entrusted with the task of preaching the gospel to the uncircumcised, just as Peter had been to the circumcised. 8 For God, who was at work in Peter as an apostle to the circumcised, was also at work in me as an apostle to the Gentiles. 9 James, Cephas and John, those esteemed as pillars, gave me and Barnabas the right hand of fellowship when they recognized the grace given to me. They agreed that we should go to the Gentiles, and they to the circumcised. 10 All they asked was that we should continue to remember the poor, the very thing I had been eager to do all along. - Galatians 2:1-10
The Catholic Encyclopedia adds this to the life of St. Paul. It only makes sense that Paul was made a bishop and apostle at the time he saw Peter in Galatians 1:18-20.
After his conversion, his baptism, and his miraculous cure Paul set about preaching to the Jews (Acts 9:19-20). He afterwards withdrew to Arabia — probably to the region south of Damascus (Galatians 1:17), doubtless less to preach than to meditate on the Scriptures. On his return to Damascus the intrigues of the Jews forced him to flee by night (2 Corinthians 11:32-33; Acts 9:23-25). He went to Jerusalem to see Peter (Galatians 1:18), but remained only fifteen days, for the snares of the Greeks threatened his life. He then left for Tarsus and is lost to sight for five or six years (Acts 9:29-30; Galatians 1:21). Barnabas went in search of him and brought him to Antioch where for a year they worked together and their apostolate was most fruitful (Acts 11:25-26). Together also they were sent to Jerusalem to carry alms to the brethren on the occasion of the famine predicted by Agabus (Acts 11:27-30). They do not seem to have found the Apostles there; these had been scattered by the persecution of Herod.