Thank you!
There seems to be some sort of an issue with WPML and your permalink setup here. The front-end language is always reported as english on the /ro/ page. I can confirm that by looking at the cookies, as well as ICL_LANGUAGE_CODE constant and the apply_filters( 'wpml_current_language', NULL ) functions are both returning “en”.
Moreover even the language switcher indicates english, and when you hover over the romanian, it tries to redirect to /ro/ro/, as it thinks it’s on an english version. If you hover the english flag, it will redirect to /ro/ as it thinks it is the english version.
I have tested by changing the URL format to parameter in WPML, then everything works just fine, including the language switcher, translations and everything. This indicates some sort of an issue with your permalink setup.
