Is it permissible for a woman to travel in her car with a foreign (non-mahram) driver, or to use public buses when her car breaks down, and is it permissible for her to learn to drive a car herself?

If a woman needs to go out and cannot find a Mahram (definition) to transport her, she should choose the lesser of two evils. If public transportation is safe, she should use it. If it is not safe due to harassment, she may drive the car herself if the need arises. As for learning to drive, it should be taught by a woman or one of her Mahrams. It is not permissible for her to ride alone with a male driver, as this constitutes unlawful seclusion (khalwa (definition)). The Prophet, peace and blessings be upon him, said: "No man is alone with a woman but the third of them is Satan."