Were Paul and Barnabas same-team allies?

Barnabas introduced Paul to the church as an ally

Right? See:
>Acts 9:26 — “When he [Paul] came to Jerusalem, he was trying to associate with the disciples; but they were all afraid of him, not believing that he was a disciple. But Barnabas took hold of him and brought him to the apostles and described to them how he had seen the Lord on the road, and that He had talked to him, and how at Damascus he had spoken out boldly in the name of Jesus.”

Barnabas got Paul to preach with him as co-pastor (for 1 year)

Right? See:
>Acts 11:21-26 — “and a large number who believed turned to the Lord. The news about them reached the ears of the church at Jerusalem, and they sent Barnabas off to Antioch. … And considerable numbers were brought to the Lord. And he left for Tarsus to look for Saul [=Paul]; and when he had found him, he brought him to Antioch And for an entire year they met with the church and taught considerable numbers; and the disciples were first called Christians in Antioch.”

Paul and Barnabas together bring financial relief for the Jerusalem church

Right? See:
>Acts 11:29-30 - ”in the proportion that any of the disciples had means, each of them determined to send a contribution for the relief of the brethren living in Judea. And this they did, sending it in charge of Barnabas and Saul to the elders.”

Paul and Barnabas go on a mission trip to Cyprus etc. together

Right? (Plausibly from the late spring of A.D. 44 to the fall of A.D. 46). See all of Acts 13-14 for the details of Paul and Barnabas’s cooperative evangelism on this first missionary journey of Paul's.

They work together in reporting to the Jerusalem church

Right? See:
>Acts 15:12 — they were listening to Barnabas and Paul as they were relating what signs and wonders God had done through them among the Gentiles. (Cf. Acts 9:26-27)

Only a side-dispute prevented more mission trips together

Right?¹ (Aside from a dispute over the dependeability of Barnabas’s cousin Mark—after all the drama and events of the first missionary journey— Barnabas and Paul were ready to work together again with the same message.)

Acts 15:36-39 — “After some days Paul said to Barnabas, ‘Let us return and visit the brethren in every city in which we proclaimed the word of the Lord, and see how they are.’ Barnabas wanted to take John, called Mark, along with them also. But Paul kept insisting that they should not take him along who had deserted them in Pamphylia and had not gone with them to the work. And there occurred such a sharp disagreement that they separated from one another, and Barnabas took Mark with him and sailed away to Cyprus.”

Many years later, Paul still praises Barnabas

Right? See:
>1 Cor 9:6 — “Or do only Barnabas and I not have a right to refrain from working?”