"The teacher can sing Chinese songs."
I think there are diiference words for Chinese as in the people, Chinese the language, Chinese the culture and Chinese the nationality
中文 translates to Chinese language. Perhaps it more accurately refers to written language though?
What's the difference between 汉语 and 中文?! Don't they both mean Chinese language?
it depends on how you interpret "can", "可以“means the teacher is allowed to sing while “会" means is able to