Language is a part of paragraph style, and also found in character style.
You nee to select fonts which support specific language features. When you buy a font, you see what features each font supports and which languages. I recommend to use only OTF fonts which allow embedding in PDFs.
For non-European languages you will need specific versions of InDesign installed. If you are a CC subscriber you can download and install those versions for Asian and ME languages, you need to change the app language in the preferences in the CC app, install, change to the next language, additional plug ins will be installed which will also work if you run the program in any other language. It will also install fonts for those language groups.