Hi Sarra and Bill,
First off, let me say that you are welcome to call me via Skype for clarification/help with this as I am not a pro and while I always understand my wrtng, it might not be clear to others. My Skype ID is in my Moodle profile.
Truthfully, this is going to get a little complicated and cluttered no matter how you decide to proceed.
Answer for item 2 first. You need to set up multiple groups containing two students, in each of your two classess and then set your assignments up for group submissions.
As for your first item, you basically have three possibilites, make duplicate copies of your course, duplicate your items, or set up access restrictions for each item.
Right off the bat, I would not duplcate the course unless you nearlly always are giving different assignments and quizzes to each of your two classes.
Duplicating assignments and quizzes - Since individual assignments and quizzes right now can only have ONE due date, if you REALLY want to use due dates, you will have to use duplicate copies of your assignments and quizzes, basically a set for each class. By using groups of two students and a grouping for each class, say Tuesday and Thursday, you can easily make it to where students see ONLY the assignment/quizzes that apply to them, which cuts down on the clutter for them, but as the teacher, you will see ALL of the topic entries. You will need to spend a little extra time and effort setting up you grade book to make sure students grades are based on the correct set of assignments and quizzes. In each of your assignments and quizzes, you would need to set the Common Module Settings for Separate Groups and set Grouping for the correct class. You would also need to set an Access Restriction, to hide assignments and quizzes that students are not responsible for.
Access Restrictions - If you DON'T want to duplicate everything, then EVERY assignment and Quiz will neeed two Access Restriction sets applied to them. One restriction set would control which grouping it applied to and a start and end date during which the students of the grouping would be able to access the assignment/quiz. The second restriction set would control access for the second grouping. Using access restrictions, you can really cut down on the clutter for students by making the items not even be visible except during the days/time they have access.
No matter which way you set things up, the teacher view will be cluttered because of all the restriction sets or duplicated assignments/quizzes with due dates being visible to the teacher all of the time.
Here is a sample view for a teacher. Topic 1 is two assignments using access restrictions. Topic 2 is two assignments for Tuesday class and two for Thursday class. The only difference is the due dates and they also use a simple access restriction to hide items for the "other" class.
This is a typical view of the same course for a student.