晚上, 老师的中国朋友回国。

one way is to omit 国 and use 中 like in the word 中药(Chinese medicine). The latter has also the meaning of Chinese style. Another way would be to place中国 in front of a noun like中国产品。It all depends on usage.

First your English... "My teacher's friend goes back to China tonight" or "Tonight my teacher's friend is going back to China". Both tenses can be used. The present tense indicates it is a fact while the other means the action is ongoing. 今晚老師的朋友要归回中国. 归回 is more formal than 回去. 中国銀行, 中国片, 中国海島 all these "China" function as adjectives.

yes you can use 中国的 to be an adjective. But sometimes we shorten to be 中国 as the adjective, it depends.

Do you mean by "My Chinese teacher's friend is coming back to China at night." ?

If yes, the correct translation will be:

我中文老师的朋友晚上回中国

我中国老师的朋友晚上回中国

中文老师：teacher who teaches you Chinese

中国老师： teacher who is from China but doesnt specifically indicate which subject he/she teaches you.