Hello René,
Thank you for reaching out, and thanks for choosing W3 Total Cache.
The options you provided in the second screenshot are correct.
However, as you mentioned, if the Browser Cache is not enabled in Performance>General settings, then those options will have no effect.
So you need to address the question to your hosting provider and ask to add the rules for expires header and cache-control for JS and CSS files, or you can ask them to disable and remove any rules on the server so that the W3 Total Cache Browser Cache module can handle everything.
Thank you!