Paul circumcised Timothy because they were telling the message of Jesus to Jews and Gentiles. Paul wanted the Jews to know that he respected the law of Moses even though the church leaders in Jerusalem had decided that Christians did not need to be circumcised.
Most people want very much to know the future, but the law of Moses said that speaking with the spirits of dead people to learn about the future is a sin. This woman seems to have been able to tell the future very well. She was a slave, and her masters made much money from her work. Paul wanted her to stop sinning, so he told the spirit to leave her. Luke does not say that she began to follow Jesus or tell us anything more about her.
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