No, there is no evidence that working at a computer damages the eyes. However, long hours of work can be fatiguing to the eyes, neck and back. Monitor glare from various light sources can also be a problem. It is often helpful to take periodic breaks, looking off in the distance and adjusting your work station (angle of the monitor, height of the chair, changing the lighting, etc.).

No, there is no scientific evidence that TV sets emit rays that are harmful to the eyes.

There is a benefit to wearing UV protective lenses--wearing them may protect against cataract formation. Clear lenses with UV protection may offer greater protection than dark lenses because they allow the eyes to be exposed to more light. This causes greater constriction of the pupil which lets less light enter the eyes.