I admit my ignorance, and so I have to ask about the cronjob time-out and cron logs...
About cronjob time-out you write: "... and the php cron script of your URL does not process a big task."
So you don't only trigger the php cron script but also WAIT for it to be completed or "PHP exit;"-ed?
If my php cron script makes a lot of checking, deleting and updating in the database plus mailing me several reports, it may be better to make several cron-jobs instead?
About cron logs: How do I exactly do to have my messages in the log?
Do I simply "PHP echo..." or do I "PHP echo..." inside a HTML-code or...?
Yes, we not only trigger the php corn script, but also wait for its finish (with cronjob timeout limit, you may check more at https://www.easycron.com/user/register).
If your php cron script handles many jobs, it should not be a problem for EasyCron to wait for its finish as long as the script isn't running longer than the cronjob timeout limit. But it's up to you about how to implement the script (do it in one or several scripts).
You can simply use "echo" or html with PHP cron script to respond the output to EasyCron to get logged.