Mandatory assignments aren't set with a separate checkbox—there's no such option in the interface—but rather through the stop lesson in the lesson settings. For the "Important Only" scenario, mark "Important Task" on the homework itself.
To make homework mandatory, open a lesson, click the gear icon, then "Lesson Settings," enable Stop Lesson, and select a condition: block future lessons until assignments are completed (this lesson, all previous lessons, or all important lessons), or block this lesson until a test is passed or a response for the previous lesson is submitted. Click Apply.
For more information on all five conditions, see How to Set Up a Stop Lesson? Automatic credit cancels manual checking, but the student's answer still needs to be submitted.