Is it permissible to kiss the head of a paternal female cousin or shake her hand over her hijab due to her old age?

It is not permissible to shake hands with a non-mahram (definition) woman or to kiss her head, even if she is elderly, because she is not a mahram. Greetings are limited to verbal communication only, such as saying "How are you?" and similar phrases. This is supported by the Prophet's (peace be upon him) saying: "I do not shake hands with women," and Aisha's (may Allah be pleased with her) saying: "By Allah, the hand of the Messenger of Allah never touched the hand of a woman," meaning non-mahram women.