I am having difficulty copying and pasting pre-translated Chinese text into InDesign.
Many of the characters are coming up as boxes in the majority of Chinese fonts offered in CC.
Font used above is Apple LiSung
I have tried to import via Apple Text Edit and format stripped the text.
Try Adobe Fangsong Std. Don't know why the others don't have all the characters.
That's happening because you have Simplified Chinese text, and are attempting to use a Traditional Chinese font.
Ellis suggests a well-made Adobe font with Trad support. If you pull down your font dropdown and scroll towards the end, you'll find fonts split into categories according to language support. The one with Apple LiSung is the Simplified category, and the one with Adobe Fangsong is the Trad category. Pick any font from that category - but know that the style of font you pick in Chinese means as much as the style of font you pick in English, and if you don't know what the conventions are, you may well choose one not entirely suited to your audience. (One of my translators likened the Chinese font choices of monolingual Anglo designers to "seeing the body text of my How To Use Your Health Care Benefits brochure laid out in Rosewood.")