How to set up a question/assignment pool for a course website?
You might want to start from the Answers module. Here are some details about it (from its project page):


  Answers enables the implementation of a Question &amp; Answer system in a Drupal site. Users can post questions and other users can answer them.


Head over to its project page for more details.

At its core, this module exists of 2 typical content types:


Question.
Answers.


The Answers module comes with integrations with other modules such as:


the Rules module, to add all sorts of business logic to fit your requirements.
the Userpoints module (and supports voting).


Here is a summary of how I'd implement what you're looking for:


the Questions and Answers are 2 content types, implemented via the Answers module.
Implement the Readings as a (3rd) content type, in which you add Entity references to the various Questions that would fit.
Implement the assignment as a (4th) content type, in which you add Entity references to the appropriate readings.


Not sure if it would be a requirement here, but I can imagine you also might want to add the Group module. Some more details about that:


you can organize the various students that attend a selected course (with group type = Class, or Training), and with each specific course implemented as a "Group".
the Group roles that would make sense in this case are:


course admin.
tutors.
students.
outsiders (= anybody else who is not (yet) involved in a specific class, but for which you want to show them something about such classes, to create awareness).



Disclosure: I'm a (co-)maintainer of the Answers module.