Translation:Are you studying?
study could more accurately be translated as "tanulmányoz" when describig what scientists do, like "studying an animal in its natural habitat" for example. When you just learn something that someone else came up with, it's always "tanul", so we don't "tanulmányozunk" for an exam.
It is not necessary to add "te". You learn/study: tanulsz. Do you study? : tanulsz? If you would add "te" to the question, it would mean you emphasize the person. For example: Te tanulsz?? Means you were surprised by the fact that he is studying. Another example why you can add "te": -What we gonna do tomorrow? - I'll rest and you'll learn tomorrow. Én pihenek, te (pedig) tanulni fogsz. Period. No controversy, no contradiction, YOU have to learn.