Did Peter know about Saul's conversion and call to the Gentiles when he preached to Cornelius?
No. Peter was not yet aware that God had saved Saul of Tarsus in a previous chapter and told him He would go to the Gentiles. When Peter preached in Cornelius's house, he was proclaiming the Gospel of the Kingdom, and the Holy Spirit fell on the Gentiles present.
Les explains that Peter certainly was not aware that in the previous chapter God had saved Saul of Tarsus and had told him He was going to go to the Gentiles. Les says he does not think Peter knew that yet. Instead, Peter was in the Gentile house of Cornelius, proclaiming the Gospel of the Kingdom. While he was still speaking, the Holy Spirit fell on all who heard the word. The believing Jews of the circumcision who came with Peter—six men, seven total—were utterly astonished that Gentiles were hearing a salvation message and believing it. God proved He was doing something totally different by having these Gentiles speak other languages.
More Questions
Did Peter know that God had already called Saul of Tarsus to go to the Gentiles?
Before Peter's visit to Cornelius, God had already saved Saul of Tarsus and told him He was going to send him to the Gentiles, and Peter did not know that yet.
What did Peter say to Cornelius about a Jew associating with a Gentile?
Peter told Cornelius at the threshold of his house that it was unlawful for him, a Jew, to keep company with a Gentile, which illustrates how strong the Jew-Gentile separation was right before God turned to the Gentiles.