"Do you guys listen to Chinese songs?"
It depends whether you are talking about Chinese culture or a specific Chinese language (remember there are at least 4). 中国 is the place. 中文 refers to generic Chinese culture and language. 汉语 is what you are studying here, what (english-speaking) westerners call 'mandarin', which is what most (but not all) Chinese people speak.
To be even more pedantic, this course seems to be more strongly influenced by Beijing/Northern Chinese dialects.