Is kissing a foreign girl's hand and greeting her unlawful or permissible? Is there a textual legal proof prohibiting that? Is it obligatory to sever ties with a friend who does that, or to strengthen the friendship with him to rectify his behavior?

What your friend did, shaking hands with and kissing the hand of a non-mahram woman, is forbidden by Sharia. It is a step towards fornication, for the Prophet, peace and blessings be upon him, said: "For one of you to be stabbed in the head with an iron needle is better for him than to touch a woman who is not lawful for him." His mention of the difference of opinion among scholars regarding the ruling on greeting a non-mahram woman refers to greeting with words, not with handshakes or kisses. Your duty is to advise your friend and inform him of the Sharia ruling. If he repents and becomes upright, then befriend him; otherwise, distance yourself from him.