I have experienced these exact issues. At this point I am honestly not sure how you can claim X / Pro is WPML ready. I have also had the issue where when I save the translation it over writes the original and vice versa.
Yesterday I ensured that the WPML settings were not set to “Synchronize page template” (WPML Settings) I also disabled all WPML plugins except the main WPML Multilingual CMS.
It seems for me this helped. I think the problem was either “Advanced Custom Fields Multilingual” plugin or having “Synchronize page template” on.
Currently I have only installed the main plugin and was able to enable “WPML String Translation”. Things now appear to be working.
Currently my steps are to create a template of the original page, copy the page to the new language, delete everything out of the builder for the new language and save, then import the template I created and start editing.
Once you have done this you will need to copy across any CSS / JS from the original language page to the new page as the templates don’t save this stuff.
Hope that helps.
Honestly working with WPML and Pro / X is a bit of a nightmare and very unstable.