What's the difference between изучать and учиться? I know that one is to study, the other is to learn but can they be used interchangeably in this context?
It this contex you can use учить (as the synonym of изучать to learn) but not учиться.
May be this link will help you to understand the difference http://www.russianforeveryone.com/Rufe/Lessons/Course1/Grammar/GramUnit5/GramUnit5_4.htm
"What language are you learning?" << That's how the native English speakers I know would express this idea. (There may be other expressions I haven't heard, naturally.) I've never heard anyone ask "Which language do you study?".