Eph. 3:2 is the key but Paul is well known for teaching on grace in his salvation message to the Gentiles.
Every epistle signed by his name opens with a proclamation of grace and peace “from God our Father, and from the Lord Jesus Christ.” In the epistles we find that we are “justified freely by [God’s] grace” (Rom. 3:24), that “where sin abounded grace did much more abound” (Rom. 5:20) that grace might reign (5:21). There we read that we are “not under the law, but under grace” (6:14), that “God is able to make all grace abound” toward us that we may “abound to every good work” (II Cor. 9:8), that it is God’s purpose for “the ages to come” to “show the exceeding riches of His grace in His kindness toward us through Christ Jesus” (Eph. 2:7). And we could go on and on adding up the evidence that “the dispensation of the grace of God” was indeed committed especially to Paul to make known to us.
Under the Law of Moses, which was still valid for the Jews in Acts, Jews were not supposed to be associated with Gentiles. As for your second question, from the incident with James and the elders in Acts 21:20-25, what probably happened was that Paul was so passionate in preaching that Gentile believers are dead to the Law, that some of those Jews also overheard and embraced it, much to the dismay of Jerusalem HQ.
