[Решено] Language selector dessapearing or languages not showing in it - Multiple and different models for ea...

Background of the issue:
I'm trying to translate my site from French to English by hand (no automatic translation yet). When I enable the option 'Show a lang selector in the footer' in WPML settings, two languages are shown. However, on a product page, even if everything is translated to English, the English choice won't appear. When I manually change the current language by adding lang=en in the URL, I can see the page is fully translated. There are sync problems between product pages: modifications in the block editor 'Gutenberg' appear on the French version but not on the English version unless I manually add lang=en in the editor URL. Additionally, when I add the 'lang selector' block in the Gutenberg editor, it appears briefly during page load and then disappears. I use string translation for translating texts in blocks and custom plugins.

Symptoms:
The language selector block disappears quickly, English language option doesn't appear on product pages, and there are synchronization issues between language versions in the Gutenberg editor.

Questions:
Why does the lang selector block disappear when the footer lang selector works well?
Why doesn't the English language option work on product pages?
Why are there sync problems between language versions in the Gutenberg editor?
Is it possible to show the English option even if some translations are missing?