Here comes word-to-word translations. "Sen de misin", is incorrect, incomplete. "Sen de mi", means "Are you too?" Like "Sen de mi, Brutus?" One more thing, you can use "Sen de öğrenci misin?" which means "Are you a student too?" Now "Sen de öğrenci mi?" is incorrect. "Öyle mi", means "Is it so?" (*) "Öyle misin", means "Are you so?" (*) (*) They are both correct. If you want to verify the situation, then use the first one. First one is more popular and usual. If you want to verify 'his' situation, then you can use the second one too. In your example, "Öyle misin" could have been used too. However, as I said, previous way is more common. In summary, "Sen de misin?" is incomplete sentence and incorrect. Dont ever use it like that. Other point you indicated is correct. They are replaceable but go for "Öyle mi?" meaning "Is it so?"