Can he kiss his seventy-year-old female cousin on the head?

You
are not allowed to shake her hand or to kiss her on the head or anywhere
else. What is allowed is for you to greet her with words only, even
if she is old, because she is not your mahram. There is nothing wrong
with you saying, “How are you? How are your children?” etc. The Messenger
(peace and blessings of Allaah
be upon him) said: “I do not shake hands with women” – and this included
old women as well as others. And ‘Aa’ishah (may Allaah be pleased with
her) said: “By Allaah, the hand of the Messenger of Allaah never touched
the hand of any woman” – meaning women who were not his mahrams, and
when he accepted their oaths of allegiance to him, it was by words only.