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Hello,
I'll help you get started while another supporter takes your case.
The title of the ticket mentions something about an HTACCESS not being writable, which tells me that something is trying to rewrite it. WPML does not ask to rewrite the HTACCESS but if the file doesn't contain the correct information and can't be edited automatically by WordPress then you will have a lot of redirection, 500 errors or 404 issues with or without WPML.
Please ask your hosting why is the file not writable and try to set the permission of the file to 644 in the meantime (all that i'm saying is something that server support should do for you and has nothing to do with WPML).
On our end i suspect that you may be encountering this issue: https://wpml.org/errata/htaccess-is-rewritten-with-language-folder/ but this could happen id another plugin is trying to rewrite the HTACCESS because it's not directly a problem created by WPML but more of a "collateral damage" from having a multilingual site (it will happen with any multilingual solution that changes the URL of the site between the languages).