I was scanning the questions and found the Jewish lineage one. Timothy was counted as Jewish because of his mother. Paul circumcised him and we know that Timothy's father was a Gentile while his mother and grandmother were Jewish. Why did Paul have Timothy circumcised after the council at Jerusalem?
As stated in, "Was Hebrew lineage ever determined through the females in history?" tracing lineage exclusively through the female line is a more recent innovation in the Jewish community that seems to have appeared sometime after the New Testament era. Prior, lineage was determined by either parent, so what is stated in Acts 16 would be accurate but not proof that at that time it was exclusively determined through the maternal line.
In regards to why Timothy was circumcised after the Jerusalem council, it is simply because Paul met Timothy after that council. Timothy wanted to join Paul, but because they were working among the Jews, Paul decided to have Timothy circumcised so that Timothy would be accepted by the Jews. "Then he came to Derbe and Lystra. And behold, a certain disciple was there, named Timothy, the son of a certain Jewish woman who believed, but his father was Greek. He was well spoken of by the brethren who were at Lystra and Iconium. Paul wanted to have him go on with him. And he took him and circumcised him because of the Jews who were in that region, for they all knew that his father was Greek" (Acts 16:1-3).