This thread is resolved. Here is a description of the problem and solution.
Problem: I'm translating my website and I set translation preferences almost everywhere to "Copy once" since I want to only change same content (the content should be copied and then I can change what I want, right?). When I'm about to publish 2nd language page I get this big notification about fields that will be copied. I click "Publish" and not everything is copied.
Solution: Make sure that the Group and Repeater types of fields are set to Copy while all the other fields need to be set to Copy, Copy once or Translate, based on your needs. Also, as explained here: https://wpml.org/documentation/related-projects/translate-sites-built-with-acf/#setting-translation-preferences-acf-fields the fields set to copy once will not appear on the Translation Editor screen.
Relevant Documentation: https://wpml.org/documentation/related-projects/translate-sites-built-with-acf/
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