How can I make the posts students make to my forum automatically go to the students’ email inboxes?
This feature is called the Subscription mode.
When a person is subscribed to a forum, it means that they will be sent email copies of every post in that forum. Users can usually choose whether or not they want to be subscribed to each forum.
However, the teacher can choose to force subscription on a particular forum then all course users will be subscribed automatically, even those that enroll at a later time.
If the teacher selects the option "Yes, initially" then all current and future course users will be subscribed initially but they can unsubscribe themselves at any time. If the teacher chooses "Yes, forever" then the forum members will not be able to unsubscribe themselves.