May women look at men, for example on screen?

Yes, seeing one another cannot be avoided in daily life, for women as for men. What matters is the gaze: it should be without desire and without any particular intent.

The verses above are addressed to men and women alike. Both are to restrain their eyes. This does not mean keeping one's eyes closed all the time. Anyone walking down the street has to see where they are going, or they will bump into others. That would be more awkward than a brief glance at a face.

What is meant is the kind of gaze. When one's eyes fall on another person, the look should carry no intent and no desire, as if it fell on an object. Interest should stay as small as possible. This applies in daily life, and it applies equally to images on a screen. Looking at something in order to learn or to stay informed is not wrong. But whoever looks at a person with a desiring gaze crosses this boundary, whether man or woman.

The question refers to a situation in which a woman was to cover herself even before a blind man. That concerns something different from the passing glance. The point is not to lead anyone into temptation without need. Not everyone has to be invited into one's home. A visitor can be attractive through his voice, his appearance or his charm, even if he himself cannot see. Creating such a situation without necessity is not wise.

Islam, then, does not forbid seeing. It teaches mindfulness. Women and men carry the same responsibility for their gaze and for the situations into which they bring themselves and others.