Let's focus first on the issue of the permalinks. I'm not being able to fully understand it, and the questions I'm asking are bringing no results. In this case, I'd like to check the website and show you what WPML offers regarding the permalinks.
I would like to look at this directly on your site. For this I would need temporary access (WP-Admin and FTP) to your site, preferably to a test/staging site where the problem has been replicated if possible.
The required fields can be found below the comments section. The information you enter is private, i.e. only you and I can see it and have access to it.
I may need to replicate your website locally. To do this, I need to temporarily install a plugin called "Duplicator" or "All in One WP Migration" on your website. This will allow me to create a copy of your website and content. Once the issue is resolved, I will delete the local website. Let me know if this works for you.
IMPORTANT
Please make a backup copy of the site files and database before giving us access.
- If you do not see the wp-admin/FTP fields, this means your post and site login details are being made PUBLIC. DO NOT post your website details if you do not see the required wp-admin/FTP fields. If you do not, ask me to enable the private box. The private box looks like this: