Sherry, you are asking some very good questions.
Due dates vary a little depending upon the type of activity that you are referring to. In my courses, I use quizzes, assignments, and forums.
For Quizzes: Look at "Timing." The "Close the quiz" date is automatically put into the Moodle Calendar for students, and students cannot take a quiz after that date.
For Assignments: Look at "Availability." There is a Due Date and a Cut-Off date. When grading assignments, those that were submitted after the Due Date are tagged as "late". I believe Cut-Off Date means students cannot submit after that date. In Moodle 3.3, there is now a "Remind me to grade by" date, which is causing me some irritation, see Tracker MDL-59798. Prior to Moodle 3.3, the assignment Due Date showed in the Calendar for students and teachers. Now, the Remind me date shows, but only when there are submittals. I hope this gets fixed.
For Forums: Look at "Ratings". There is a Restrict Ratings From and a Restrict Ratings To set of dates. Neither of these are put into the Calendar, but I have a Tracker Item MDL-31355 where I am asking for a Due Date that automatically goes into the Calendar. Neither of these two dates restrict discussions, which I like, but the "From" date does help the grader (or teacher) see which posts are late by not allowing rating. Forums do provide a "Restrict Access," which can be a date. I have never used it (yet.)
There is also a Moodle User's Group project proposal that is attempting to address dates. I am one who would like to see a somewhat consistent way of automatically putting dates in the Calendar for all Moodle activities. It's a complex situation since Moodle also has a Dashboard, Upcoming Events, and other features that are connected to "dates." But we (i.e., the moodle community) needs to get our arms around dates. I haven't found time to help develop the new MUG proposal, yet.
"Restrict Access" also can be set for Assignments and Quizzes. I haven't used these, and therefore can't explain what they do, but Moodle does provide a method of allowing access to activities based upon previous activities being completed, and I think that this is where "Restrict Access" comes into play. Also, I haven't used the other moodle Activities of Chat, Choice, Database, Feedback, Glossary, Lesson, Survey, etc., to know how they handle due dates. You can see that it really does get complex.
Consider voting for my tracker items.
Maybe others can jump in and help clarify what I have shared.