Were the early Jewish believers under Peter's preaching still keeping the Law?
Yes. The early Jewish believers who came under Peter's preaching remained Law-keeping Jews. They believed Jesus was the Christ, the Messiah of Israel, but they were not yet believers of Paul's Gospel. They continued under the Law, and this distinction explains the conflict in Acts 15.
Les explains that the Jews entering Gentile congregations in Acts 15 were not the Orthodox or Pharisees, who would have nothing to do with Gentiles and viewed them as dirty dogs. Rather, they were Jewish believers that Jesus was the Christ. They were not believers of Paul's Gospel; they still believed Jesus was the Messiah of Israel. Therefore, they remained under the Law. Les says that those early Jewish believers under Peter's preaching were still Law-keeping Jews, and though many do not realize it, it is very evident.
And certain men which came down from Judaea taught the brethren, and said, Except ye be circumcised after the manner of Moses, ye cannot be saved.
More Questions
Who were the Jews that came into Gentile congregations teaching circumcision and the Law?
Those coming into the Gentile congregations were Jewish believers that Jesus was the Christ, not believers of Paul's Gospel, but still believing Jesus was the Messiah of Israel.
Did the Judaizers suggest law-keeping as an optional way to be a better Christian?
The Judaizers did not merely suggest that keeping the Law could make someone a better follower of Christ; they commanded it and attached salvation to it.