Did Peter and those with him tell Israel that God was dealing with the Gentiles directly?

No. Peter and those who went with him did not tell Israel that God was now dealing with the Gentiles directly. For another eight or ten years they said nothing to the children of Israel about God dealing with Gentiles on His own ground, not on the basis of using the nation of Israel.

Les explains that after Cornelius' house, the Jews should have gone back to Jerusalem and spread the word that God was now ready to turn to the Gentiles without Israel. But they did not. Turning to Acts chapter 15, Les points out that Peter and those who evidently went with him had never said a word for another eight or ten years. Not one word did they cast among the children of Israel that God was now dealing with the Gentiles on His own ground and not on the basis of using the nation of Israel.

Acts 15

How did Peter publicly respond to God saving the Gentiles apart from Israel?

Peter did not publicly announce it to Israel. After Cornelius' household, he and those with him remained silent among the children of Israel for another eight or ten years, never casting a word that God was now dealing with Gentiles on His own ground apart from the nation of Israel.