Is it obligatory to complete the fast and make up the day if I hesitated about the intention to fast from the night before, then listened to music after Fajr, knowing that it is a make-up day for Ramadan?

For a fast to be valid, the intention (niyyah) must be firm. If a person fasting hesitates in their intention, uncertain whether to fast that day as a make-up (qada) or not, their fast is not valid. The day remains a debt upon them, and they must make it up. It is permissible to complete a fast as a voluntary (tatawwu') act if the intention was made before dawn. Listening to music or watching forbidden things does not invalidate the fast, but one must avoid them.