Always study all the materials in each box carefully. I also recommend that you print them out for further reference. 

As for "Handouts", these should be printed out, since you are expected to study them before coming to class. 

Online quizzes are recommended for the dates specified and must be done in the examination period at the latest before students are given their credits.. 

Additional online activities should also be done, because the more you practise, the better, of course! 

Do not forget that it is not enough to work with your online course materials only! You should always study relevant chapters in the required textbooks, i.e. the books by Greenbaum and Quirk, Chalker, and Gethin! 
I recommend that you first study the relevant chapters in the reference textbooks (see "Homework" in each box for more detail - it always tells you what to study/prepare for the next "box") - having done this, you can then go to online course and work with the corresponding handouts, which should help to sum up / revise / clear up the content of the required textbooks (i.e. Greenbaum and Quirk, Chalker, and Gethin).