Is it forbidden to follow a person's news and view their pictures on Facebook without speaking to them?

If the inclination is not a result of your own earning (effort) and does not lead to something unlawful, then there is no sin upon you. However, you are obligated to repel this thought and to fill your time with that which is beneficial. As for looking at his picture, it is forbidden by Islamic law, based on the Almighty's saying: "And tell the believing women to lower their gaze." So, looking at a picture takes the same ruling as looking at foreign men.