For example, can you use this expression to say "I don't mind/care if you listen to music." or other things like that?

Bonjour Julie, I am unable to locate anything in the lesson that discusses the idiom use in a longer sentence; however, ça m'est egal si tu écoutes de la musique pendant nous travaillons. seems perfectly plausible. Of course, it is possible that there is a more correct way to utilize the idiom to say this phrase. I am hedging my answer here because I do not know all of the idiom uses correctly. Bonne chance !

Alors, I found an example phrase in Collins-Robert. «Elle a le dos rond, et le bide assorti, les pieds en compote et le moral au diapason Dis donc, Josyane, ça t'est égal ?» As can be noticed from this phrase, it is a response to a statement, albeit, with a question. Perhaps this idiom is intended to be simply used as a response, not unlike yes or no.

Merci, Laura !

Thank you both for taking the time to answer my question :)