Are the sins that a sister might commit (such as publishing pictures of women, downloading songs, or teaching her friends how to use Facebook and use it improperly) considered ongoing sins for the questioner, knowing that the original intention was to teach her how to use the computer?

There is no sin upon you if your sister publishes pictures of women or commits a reprehensible act via the internet, as long as you do not assist her or approve of her actions. Your teaching her how to access the internet does not make you bear the sin of her actions, because you taught her for a legitimate purpose. However, you must persistently advise her, enjoin her to good, and forbid her from evil.