Hi Dominik,
Regarding WPML – I’m yet to test this out myself, but have mixed reports from users. I believe it depends on your URL structure within WPML, but it’s something I’m looking to build solid support for, as such a popular plugin.
AJAX scripts generally work fine, but there are so many possibilities as to what the script is doing/how the content it returns is used in the page, etc.
I would suggest trying the current 5.8 version of the plugin with the “Same server” mode. It will give you a quick test of how your site will look, published as static HTML.
If you want to get a jump start on version 5.9 and help shape its development, the latest build is here:
https://drive.google.com/open?id=18TUAfn3ARliHENrvu55J4pX-ji1oTvoc
Which is a major rewrite under the surface and will be what any WPML support is based on.
Either way, I’m happy to discuss more and help you on your WP 2 static journey, please join me in our support/development community at https://wp2static.com/community/ for a chat.
Cheers,
Leon