This thread is resolved. Here is a description of the problem and solution.
Internal server error caused by misconfigured .htaccess with W3 Total Cache
W3TC is one of the best caching plugins for WordPress, and it is compatible with WPML.
Please make sure that you are following our instructions and suggestions on how to work with WPML and the w3TC plugin. You can see the documentation here.
Please note. The W3TC is a complex plugin that you need to know how to configure to work correctly. WPML is also compatible with other caching plugins. For example, the WP Super Cache. https://wpml.org/plugin/wp-super-cache/. This plugin is more simple to configure, so you might want to consider using it.
This is the technical support forum for WPML - the multilingual WordPress plugin.