Verified answer

"watashi no hima na toki DE ongaku wo kikimasu. sore kara, nihongo WO benkyou shimasu"

私の暇な時で音楽を聞きます。それから、日本語を勉強します。

Use de in the first sentence because it means in or during. Wa is a subject indicator, so if you have wa it means something like "my free time listens to music" instead of "I listen to music in my free time". For the second sentence, you say nihongo wo, since nihongo is the object of your study. You also don't need the wo between benkyou and suru.