Is it possible to introduce a workflow or some rules when the users try to post a new event in the calendar?
When an user tries to post an event in the calendar it has to be approved by an other user who had permission to do that. Is it possible? Can I parametrize that?
Out-of-the-box you can (as an Admin) create a folder rule on the "calendar" folder within a site so that whenever a new item is added (which will be an .ics file) then a workflow will be started. It would then be up to you to create the workflow that you want to determine how to handle that new .ics file.
Unfortunately I don't think it's possible out of the box to set up the folder rules without providing access to the repository browser - but it should be possible to configure access to the repository page for regular users.