Thank you for your answer. php.ini did not have those directive. I added it and then configured the crontab.
Will see now if there are some errors in 5 minutes.
Update: no news from the crontab. Simulating the crontab command i have this error:
PHP Warning: session_start(): open(/var/lib/php/session/sess_pelc2mj10af9spobag5foq9tk6, O_RDWR) failed: Permission denied (13) in /var/www/vhosts/support.medieval-europe.eu/httpdocs/main.inc.php on line 48
PHP Warning: Unknown: open(/var/lib/php/session/sess_pelc2mj10af9spobag5foq9tk6, O_RDWR) failed: Permission denied (13) in Unknown on line 0
PHP Warning: Unknown: Failed to write session data (files). Please verify that the current setting of session.save_path is correct (/var/lib/php/session) in Unknown on line 0
update: i changed session.save_path for the cmdline php to /var/tmp. Now there is no more errors, but still emails aren't fetched nor error displayed...