can you share a link to your site where we can see the issue?
You can edit your original topic and use the Site URL field to share the link in private.
Other things are working fine.
Only issue that in live site
if plugin is activated the https://algamar.de/de/rezepte-mit-algen/ in this images are not display and if I deactivate the plugin from back-end then images started displaying again.
Any plugin that performs extra server requests or database queries is going to impact your site performance. So yes i would expect WPML to have an impact on your site performance.
You may want to speak with your host to see if they provide dedicated servers for a multi language woocommerce site.