What is the ruling on studying a language in the West, with mixing, for the purpose of learning the language? And what is the ruling on teaching driving and driving without a mahram?

It is not permissible for a woman to travel a distance that allows for the shortening of prayers unless she is accompanied by a محرم (unmarriageable kin). As for co-educational study, it has conditions for its permissibility, just as a woman driving a car is not prohibited if specific conditions are met.