Thanks for your suggestions, Stiofan, sure they will improve the performance.
I just checked the cache dirs on the server. No cached pages in ‘wp-content/cache’ except the file ‘gdb-advanced-cache’, and >30.000 JS files in ‘wp-content/booster_cache’.
Update: when inspecting the cache dir on the server I see that some pages have been cached. Just a few, less than 1% of all pageviews. I also checked the error log, nothing found.