Is it permissible to offer greetings of peace to a foreign man upon entering a car, especially if I am asked to do so?

It is not permissible for a woman to be alone with a non-mahram man in a car, because that constitutes a state of khalwa (private seclusion). However, if there are other women with her and there is no fear of fitna (temptation/strife), then it is permissible. It is also permissible for her to offer greetings of peace (salam) to a non-mahram man when there is no fear of fitna. If there is a fear of fitna through the greeting, then it is not permissible to initiate it or to return it.