Hi,
You use the plugin Polylang to add the multi-language on your site, you need to see how this plug-in works.
https://polylang.pro/doc/
To the product can be operated in both English and Vietnamese versions, you need to create 2 products version so that they can work when redirecting. (product-vn, product-en).
Eg: You have a product category name"Ba lô học sinh Tomi" (Vietnamese version) ------> I have translated a product category corresponding "Tomi student bag" http://prntscr.com/jpdssr.
Later, you go to Product create a product English version and assign to "Tomi student bag".
---> You go to Home Page and get the shortcode Product in category tab and check again.
- With Latest News:
Similar, you go to Posts -> Add new Post.
http://prntscr.com/jpdwzp
Thanks.