Is this student's love for her teacher merely an attachment to her, or is it love for the sake of Allah? And how can she repent to Allah and remove from her heart attachment to anyone other than Him, Glorified be He, if it is an attachment?

The reason for your love for the teacher is her righteousness and her diligence in performing the Duha prayer. This love for the sake of Allah persists despite her occasional coldness, which is proof that it is love for the sake of Allah. So there is no need for worry or confusion.