How can I have translations for my subdomain
I'd double-check your index.php files for all domains and make sure they're all using the correct handle in the define('CRAFT_SITE') code. Sometimes I copy/paste files between sites and forget to update the site-specific variables.

I'd also make sure the Base URL for each site is correct in the settings. 

Also make sure the section your homepage uses isn't set to the wrong propagation method.