Is it still related to images? I recommend disabling the WPML Media plugin and try the images on the translated pages again.
And would you mind providing a video recording for all of these issues? I couldn't try it directly since you said it automatically copies them (overwriting) and I'm afraid I may contribute to issues if I do that.
But I do deactivate the
Advanced Custom Fields Multilingual plugin as it caused errors for text element that makes editing not possible.
I also created an X TEST page to see if the overwriting and automatic copies are occurring and it didn't happen on first 3 saves and loads, but then it happens and I can't change the content anymore. So perhaps this isn't related to translation but could be saving issue since it's too slow on my end. And on my end, it's the Latvian is the one broken as it won't save the changes, it remains in English after 4th save and page reloads.
Your site is slow and the builder changes won't take effect instantly. I had to wait just for the added short-text to regenerate a preview. I recommend increasing your site's memory limit as for step 8 as @thai's recommended.
With this many issues, I recommend cloning your site in staging. It's better to test it there before adding more issues. You could do that by using All in one migration plugin, we're not migrating, but we just need to export the site using that plugin and import it to a new Wordpress installation (in sub-folder or sub-domain). Then please provide the FTP login credentials for that staging.