Hay, Moses Young, how you doing this very, very cold morning?
You asked concerning this verse, "Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost: Teaching them to observe all things whatsoever I have commanded you: and, lo, I am with you always, even unto the end of the world. Amen."
I agree with you, there does appear to be a slight contradiction. I came up with two possibilities. The first, Matthew 10:5 was before the cross, and Matthew 28:19-20 was after the cross. Peter's interaction was very limited concerning the Gentiles, but he did meet with them at the house of Cornelius.
My second thought on the subject is found in Acts 2 on the day of Pentecost (Shavout). The apostles were gathered together in the area of the Temple mount, standing before thousands of Jews that had come from around the Roman Empire. They had come to Jerusalem to celebrate Pentecost which is several months after Passover. You know the story, these thousands of Jews heard the gospel in their own language, then returned to their own countries and through them the Gospel of Jesus Christ was spread among both the Jews and Gentiles. So, by proxy the disciples spread the gospel to the Gentiles. Your thoughts.
I'll get back to you on your second question. Have to pick up a few prescriptions.