Hi there. In order for any of the regular, scheduled activities Moodle offers to occur, there must be a something running at regular intervals on your computer to trigger the processing of these events.
In other words, all these scheduled things are only checked and processed when the moodle admin/cron.php file is executed.
So, if you set up a cron job to run (lets say) every fifteen minutes, and that job executes the moodle admin/cron.php script, then all your forum emails, and scheduled events and backups will just work as you've scheduled them!
Have a look at the Set up cron page, as suggested, and post back here if you have trouble.