Grammar rules don’t change much. There was a time that in a formal article like this, using a contraction like I did in that first sentence would’ve been taboo, but it isn’t anymore. The need for subject/verb agreement, the proper use of pronouns, the form of an infinitive, are all the same. When we were in school, we reviewed them year after year! That was most obvious in high school for me when we spent half the year reading literature we had never read, then half the year in grammar studies reviewing what we had always reviewed.
In Acts, Luke does some repeating. I suggest he repeats for the same reason we repeat: to reinforce something that is important. After Luke told the story of the conversions of Peter (to be willing to go the Gentiles with the gospel) and Cornelius (to the Way), he used the report of Peter to the critical, circumcised believers in Jerusalem to repeat the message to the readers of Acts. What message did Luke want his readers to get? He wanted them to know that God intended for the gospel to be preached to non-Jews. He wanted them to know that God wanted to save all of the lost.
Notice the effectiveness of Peter’s explanation: “When they heard this, they had no further objections and praised God, saying, ‘So then, God has granted even the Gentiles repentance unto life.’”
Praise from their lips was not all they offered, though. Luke tells us that those who had scattered in connection with the stoning of Stephen only told the message to the Jews. Now, however, “Men from Cyprus and Cyrene, went to Antioch and began to speak to Greeks also, telling them the good news about the Lord Jesus. The Lord's hand was with them, and a great number of people believed and turned to the Lord."
Be careful not to read Acts simply from an historical perspective. If you read this as simply an historical account, you will conclude, “The gospel really began to be preached to the Gentiles here.” If you read it like you need to, you will conclude, “I need to be telling the message to all the lost.”
Luke will play this same song again. Look for it. But don’t just look for the message - do what you see! The poor and the rich, the majority and the minority, the regular and the not-so-regular people need the gospel that you’ve received.