What is the ruling on shaking hands with a woman and looking at female relatives while speaking with them in Islam?

It is not permissible to look at a non-mahram (definition) woman, whether she is a relative or not, due to the generality of Allah’s saying: "Tell the believing men to lower their gaze." As for greeting a non-mahram woman, some scholars have permitted it absolutely, provided there is no fear of temptation. The majority, however, have permitted it for elderly women but not for young women, due to the fear of temptation with young women and its absence with elderly women.