Is it permissible for a Muslim woman to learn driving from a non-mahram man in a European country, with the possibility of her hand being touched, and is there any evidence for its permissibility or prohibition?

It is not permissible for a Muslim woman to learn to drive from a non-mahram (definition) man if it entails khulwa (private seclusion) or touch, whether in a European country or elsewhere. The evidence for this is the Prophet's (peace and blessings be upon him) saying: "No man is alone with a woman except with a mahram," and "No man is alone with a woman but Satan is the third of them." However, if there is no khulwa or touch involved, then it is permissible for a woman to learn to drive from a man, provided that the শরী'আ-compliant regulations are adhered to, such as proper covering (ستر) and avoiding touch and private seclusion.