Regarding music: Would listening to female Christian vocal artists break the command for women not to teach men?
Much would depend on the message of the song. If the song demands that the listeners do as the singer directs, then there would be a problem. "A woman must quietly receive instruction with entire submissiveness. But I do not allow a woman to teach or exercise authority over a man, but to remain quiet" (I Timothy 2:10-11). A song that encourages other women to live godly lives or one that expresses a love for God is not usurping any authority over men, even if a man might listen to the recording.
Consider that Aquilla and Priscilla thought Apollos privately (Acts 18:26). That private teaching did not place Priscilla as an authority over Apollos, and so did not violate I Timothy 2:10-11. It is the way the teaching is done that makes the difference.
In the same way, if a Christian woman wrote an article on some topic, nothing wrong was done even if men might read it and learn something from it. The key is how the information is presented.