Is it permissible for a woman to learn driving from a non-mahram man, and is his touching her hand with the intention of teaching during the initial lessons permissible?

It is permissible for a woman to learn to drive a car when there is a need, and it is permissible for a non-mahram man to teach her, provided she adheres to the legal hijab and refrains from using perfume, and that a mahram is present to prevent seclusion. She should take precautions as much as possible to avoid physical contact, and if it occurs unintentionally, there is no sin, for Allah says: "So fear Allah as much as you are able."