Do many Chinese songs cover foreign countries? Or do foreign countries cover Chinese ones? Why is it not infringing?

China covers many foreign songs, such as Happy Old Home

Foreign countries cover China quite a bit, such as Kiss Goodbye

China covers China even more, such as Guo Meimei's, which is basically a cover

Covers and changes have to be done with the copyright holder's permission or by paying the copyright holder the appropriate fee! Anything that doesn't go through that process is copyright infringement. There is also the case of changing the lyrics or the tune, and if the original author is credited and the song is not used for commercial purposes, it is not considered an infringement.